User:Methodios/Bernburg 1
Bernburg 1
Pawel Kröger
editer legte zuvor das Abitur im Fach Mathematik ab
1972 DDR Pawel Kröger 29 July 1958
Jahr Land P1 P2 P3 P4 P5 P6 Summe Rang Preis
Abs Rang
- 1973 Deutsche Demokratische Republik 6 0 1 6 6 8 27 19 85,48% Silbermedaille
- 1972 Deutsche Demokratische Republik 5 6 7 7 7 8 40 1 100,00% Goldmedaille, Spezialpreis
http://www.imo-official.org/participant_r.aspx?id=10230
educated at University of Erlangen-Nuremberg
academic degree Doctor rerum naturalium end time 1986 1 reference DNB editions 870990586
- Vergleichssätze für Diffusionsprozesse, Kröger, Pawel (Verfasser), Erscheinungsdatum: 1986, Umfang/Format 109 S. ; 21 cm, Hochschulschrift Erlangen, Nürnberg, Univ., Diss., 1986, Schlagwörter: Differentialgleichungen / Diffusionsprozesse ; Diffusion / Vergleichssätze f. ̃prozesse, Sachgruppe(n) 27 Mathematik ; 0300 Mathematik, Physik, Astronomie https://d-nb.info/870990586
- doctoral advisor: Heinz Bauer, 1 reference, stated in Mathematics Genealogy Project
https://mathgenealogy.org/id.php?id=26511
Bestätigte E-Mail-Adresse bei uni-jena.de - 20 Arbeiten von 1989 bis 2018
https://scholar.google.com/citations?user=c-k-ujUAAAAJ
Kröger, Pawel
MR Author ID: 244139
Earliest Indexed Publication: 1975
Total Publications: 23
Total Citations: 199
https://mathscinet.ams.org/mathscinet/MRAuthorID/244139
Photography
edit
Photography
"Leipzig, Universität, Mathematikvorlesung Zentralbild Raphael 30.1.70 Leipzig: Jüngster Mathematikstudent- Mit elf Jahren studiert der Leipziger Schüler Pawel Kröger bereits an der Sektion Mathematik der Karl-Marx-Universität. Er kann mit seinen Kommilitonen des ersten Studienjahres Schritt halten. II DDR M Vorigen Jahr legte Pawel das Abitur im Fach Mathematik ab, den übrigen Unterricht erhält er jedoch seinem Alter entsprechend in der Klasse 5a der Leipziger Nikolai-Rumjanzew-Oberschule, wo seine Mutter als Lehrerin tätig ist. Bitte beachten Sie dazu unser Foto J0130-07-1N"
See also:
https://geheimtipp-leipzig.de/neuigkeiten-aus-der-vergangenheit/
In der LVZ vom 1. Februar 1970 lernen wir den damals elfjährigen Pawel Kröger kennen, der seit September 1969 an der Sektion Mathematik der Karl-Marx-Universität Leipzig studierte und ansonsten in eine 5. Klasse der Nikolai-Rumjanzew-Oberschule (Ratzelstraße) ging. Was ist wohl aus diesem Mathe-As geworden?
https://geheimtipp-leipzig.de/neuigkeiten-aus-der-vergangenheit/zeitung-be-1/
Methodios (Diskussion) 12:38, 23 November 2022 (UTC)
Biography
edit29. Juli 1958
Besuchte Schulen von Pawel
1965-1969:
55. POS "Nikolai Rumjanzew" Grünau-Siedlung, Leipzig
1969-1973:
49. POS "Ho Chi Minh", Leipzig
https://www.stayfriends.de/Personen/Leipzig/Pawel-Kroeger-P-LEKGJ-P
Dr. nat. 1986 Erlangen
"Kröger, Pawel: Goldmedaille und Zusatzpreis 14. IMO, Silbermedaille 15. IMO. 49.
OS Leipzig, ab 70 Schule und Studium der Mathematik nach Sonderplan an der Uni Leipzig, 77 Diplom, danach Dissertationsprojekt (Betreuer G. Laßner),
- Gerd Laßner (1940–2005), deutscher Mathematiker - https://de.wikipedia.org/wiki/Lassner
79 Ausreise in die BRD,
Promotion (86, Betreuer H. Bauer) und Habilitation in Mathematik, bis 95 an der Uni Erlangen,
95–98 USA,
seit 98 Valparaíso (Chile)
Schulzeit: langjahriger Frühstarter, bereits als Schüler der Klasse 4 Teilnehmer der DDR-Olympiade in Klasse 10, ab 70 Schule und Studium der Mathematik nach Sonderplan an der Uni Leipzig (Betreuung durch R. Schimming, 71–73 K. Schmudgen, Diplombetreuer G. Laßner)"
https://lsgm.uni-leipzig.de/lsgm/Geschichte/IMO-Leipzig.pdf
Antecedentes académicos email: [email protected]
Participación en olimpiadas de matemáticas:
IMO 1972: Medalla de oro, Premio especial imo-official1972
IMO 1973: Medalla de plata imo-official1973
Doctorado Universität Erlangen-Nürnberg 1986
Habilitación Universität Erlangen-Nürnberg 1993
Coordinaciones UTFSM:
MAT-023 semestres 1-2000, 2-2007, 1-2008, 2-2008
MAT-022 semestres 2-2003, 1-2004
MAT-024 semestre 2-2000
Página del curso MAT-023: MAT-023 2-2008
Maestro destacado UTFSM: 2007, 2008, 2009, 2012, 2013
Investigación, links: Research Pawel Kröger
Autor Pawel Kröger en scholar.google.com: Pawel Kröger
Pawel Kröger en ResearchGate
https://sites.google.com/site/pawelkroeger/curriculum-1
Dr. rer. nat. Friedrich-Alexander-Universität Erlangen-Nürnberg 1986 Germany
Dissertation: Vergleichssätze für Diffusionsprozesse
Advisor: Heinz Bauer
No students known.
https://www.mathgenealogy.org/id.php?id=26511
28
Publications
1,233
Reads
410
Citations
Introduction
Pawel does research in Spectral Geometry, Analysis and Stochastic Processes.
https://sites.google.com/site/pawelkroeger
Skills and Expertise
Mathematical Analysis
Real and Complex Analysis
Publications
edithttps://www.researchgate.net/profile/Pawel-Kroeger
Publications (28)
Regular Boundary Points and Exit Distributions for Parabolic Differential Operators
editRegular Boundary Points and Exit Distributions for Parabolic Differential Operators
Article
Full-text available
Jul 2018
Pawel Kröger
Abstract
We show that the regularity of a boundary point for a parabolic differential operator in divergence form is under some geometric assumptions equivalent to the property that the density of the exit distribution for a time reversed process vanishes at that point. We give regularity and irregularity criterions for equations with variable coefficients. Thus, the known result on the Fulks measure that states that the density with respect to the Lebesgue measure vanishes at the point opposite to the center of the heat ball (see Fulks (Proc. Am. Math. Soc. 17, 6–11 1966)) can be extended to exit distributions for more general regions and parabolic differential operators.
Keywords Regular boundary points ·Exit distributionsMathematics Subject Classification (2010) 31B25 ·60J60
View
July 2018 Potential Analysis 49(3)
49(3)
DOI:10.1007/s11118-017-9652-8
Received: 29 April 2016 / Accepted: 4 September 2017 / Published online: 9 September 2017 © Springer Science Business Media B.V. 2017
Pawel Kröger
Departamento de Matematica, UTFSM, Valparaıso, Chile
FIG. 1: (a) Complex Q 2 plane; (b) complex z plane where z = ln(Q 2 /Q...
FIG. 2: |β(F (z))| as a function of z = x iy for the beta function...
FIG. 9: The function e Fr(t) appearing in the integral (A14) of r (LB)...
Perturbative QCD in acceptable schemes with holomorphic coupling
editPerturbative QCD in acceptable schemes with holomorphic coupling
Article
Full-text available
May 2015
Carlos Contreras
G. Cvetic
Koegerler Reinhart[...]
Oscar Orellana
View
World Scientific
International Journal of Modern Physics A
30(15)
DOI:10.1142/S0217751X15500827
Authors:
Carlos Contreras
Universidad Técnica Federico Santa María Valparaíso, Chile
G. Cvetic
Universidad Técnica Federico Santa María
Koegerler Reinhart
Pawel Kröger
Abstract and Figures
Perturbative QCD in mass independent schemes leads in general to running coupling a(Q²) which is nonanalytic (nonholomorphic) in the regime of low spacelike momenta |Q²|≲1 GeV². Such (Landau) singularities are inconvenient in the following sense: evaluations of spacelike physical quantities 𝒟(Q²) with such a running coupling a(κQ²)(κ~1) give us expressions with the same kind of singularities, while the general principles of local quantum field theory require that the mentioned physical quantities have no such singularities. In a previous work, certain classes of perturbative mass independent beta functions were found such that the resulting coupling was holomorphic. However, the resulting perturbation series showed explosive increase of coefficients already at N⁴LO order, as a consequence of the requirement that the theory reproduce the correct value of the τ lepton semihadronic strangeless decay ratio rτ. In this paper, we successfully extend the construction to specific classes of perturbative beta functions such that the perturbation series do not show explosive increase of coefficients, the perturbative coupling is holomorphic, and the correct value of rτ is reproduced. In addition, we extract, with Borel sum rule analysis of the V A channel of the semihadronic strangeless decays of τ lepton, reasonable values of the corresponding D = 4 and D = 6 condensates.
(a) Complex Q 2 plane; (b) complex z plane where z = ln(Q 2 /Q 2 in ); the non-timelike stripe is −π ≤ Imz < π.
(a) Complex Q 2 plane; (b) complex z plane where z = ln(Q 2 /Q 2 in ); the non-timelike stripe is −π ≤ Imz < π. … |β(F (z))| as a function of z = x iy for the beta function (8) with f (Y ) having the form (10) with: (a) r 2 = 0; (b) r 2 = −2.
|β(F (z))| as a function of z = x iy for the beta function (8) with f (Y ) having the form (10) with: (a) r 2 = 0; (b) r 2 = −2. … The function e Fr(t) appearing in the integral (A14) of r (LB) τ : (a) as function of t; (b) as function of ln t.
The function e Fr(t) appearing in the integral (A14) of r (LB) τ : (a) as function of t; (b) as function of ln t. … Figures - uploaded by G. Cvetic
Invariance of cones and comparison results for some classes of diffusion processes
editInvariance of cones and comparison results for some classes of diffusion processes
Chapter
Apr 2006
Pawel Kröger
Without Abstract
View
DOI:10.1007/BFb0043783
In book: Stochastic Differential Systems (pp.171-182)
Authors: Pawel Kröger
An extension of Günther?s volume comparison theorem
editAn extension of Günther?s volume comparison theorem
https://www.researchgate.net/publication/225889482_An_extension_of_Gnthers_volume_comparison_theorem
Article
Aug 2004
Pawel Kröger
Abstract
The aim of this note if to give an extension of a classical volume comparison theorem for Riemannian manifolds with sectional curvature bounded above (see Günther, P. ‘‘Einige Sätze über das Volumenelement eines Riemannschen Raumes’’, Publ. Math. Debrecen 7, 78–93 (1960)). For the case of a n-dimensional simply connected complete Riemannian manifold with nonpositive sectional curvature our theorem states that the function t↦area(S t (p))/t n−2 is convex for every p∈M where S t (p) denotes the sphere of radius t with center p. In view of area(S 0 (p))=0, it is easy to see that our theorem implies the classical result. A similar result holds true for simply connected manifolds with sectional curvature bounded above by a negative constant.
View
August 2004
Mathematische Annalen
329(4):593-596
DOI:10.1007/s00208-004-0520-7
A short constructive proof of Jordan's decomposition theorem
editA short constructive proof of Jordan's decomposition theorem
Article
Jan 2004
Pawel Kröger
Abstract
Although there are many simple proofs of Jordan's decomposition theorem in the literature (see [1], the references mentioned there, and [2]), our proof seems to be even more elementary. In fact, all we need is the theorem on the dimensions of rang and kernel and the existence of eigenvalues of a linear transformation on a nontrivial finite dimensional complex vector space.
View
January 2004
SourcearXiv
Gradient Estimates for the Ground State Schrödinger Eigenfunction and Applications
editGradient Estimates for the Ground State Schrödinger Eigenfunction and Applications
Article
Jul 2002
Rodrigo Ba
Nuelos And
Pawel Kröger
Abstract
Introduction be a bounded convex domain in Euclidean space R : Consider the Schr?odinger operator 4 V for a nonnegative convex potential V under Dirichlet boundary conditions. Under these assumptions the eigenvalues are discrete and satisfy 0 < 3; : : : . When the potential is identically zero we will just write i; for these eigenvalues. The quantity is called the spectral gap. It was conjectured by M. van den Berg [4] that can be estimated below by 3 where d denotes the diameter of (See also [1], [2] and Problem 44 in [13].) The lower bound =4d was obtained in [11]. This bound was subsequently improvement to in [10] (see also [8]). For V = 0 and planar convex domains which are symmetric in both axes, Smits [12] obtained a similar lower bound with the diameter replaced by the length of the longest axes of symmetry. The symmetry assumption is needed in order to apply a result by L. Payne [9] which guarantees the existence of an
View
July 2002
Authors:
Rodrigo Ba
Nuelos And
Pawel Kröger
Gradient Estimates for the Ground State Schrödinger Eigenfunction and Applications
editGradient Estimates for the Ground State Schrödinger Eigenfunction and Applications
Article
Full-text available
Dec 2001
Rodrigo Banuelos
Pawel Kröger
Abstract
Let Ω be a planar convex domain which is symmetric with respect to each coordinate axes. In this paper we give a simple and very short proof, based on the maximum principle, of the sharp lower bound for the spectral gap of the Dirichlet Laplacian in Ω.
View
December 2001
Communications in Mathematical Physics
224(2):545-550
DOI:10.1007/s002200100551
Authors:
Rodrigo Banuelos
Purdue University
Pawel Kröger
Mathematics Department, Purdue University, West Lafayette, IN 47907 E-mail address:[email protected]
Departamento de Matematica, UTFSM, Valparaıso, Chile E-mail address:[email protected]
On the Placement of an Obstacle or a Well so as to Optimize the Fundamental Eigenvalue Evans M. Harrell II
editOn the Placement of an Obstacle or a Well so as to Optimize the Fundamental Eigenvalue Evans M. Harrell II
Article
Full-text available
Jun 2000
Evans Harrell
Pawel Kröger
Kazuhiro Kurata
Abstract
We investigate how to place an obstacle B within a domain# in Euclidean space so as to maximize or minimize the principal Dirichlet eigenvalue for the Laplacian on# n B. The shape of B is #xed a priori #usually as a ball#, and only its position varies. We establish that for a certain class of domains the minimizing B is in contact with @ while the maximizing B is in the interior, typically at the center #supposing that the domain is su#ciently symmetric for this statement to be meaningful#. Under special circumstances we can characterize the optimizing con#gurations with multiple obstacles. Our method relies on the Hadamard perturbation formula and a moving plane analysis. Similar facts are proved when the hard obstacle is replaced by a central nonnegative potential function supported in B, and we consider the Schr#odinger operator with this potential. Complementary facts are proved when the obstacle is replaced by a central nonpositive potential function. I. Introduction In thi..
View
June 2000
SIAM Journal on Mathematical Analysis
33(1)
DOI:10.1137/S0036141099357574
SourceCiteSeer
Authors:
Evans Harrell
Georgia Institute of Technology
Pawel Kröger
Kazuhiro Kurata
Tokyo Metropolitan Universit
On upper bounds for high order Neumann eigenvalues of convex domains in Euclidean space
editOn upper bounds for high order Neumann eigenvalues of convex domains in Euclidean space
Article
Jun 1999
Pawel Kröger
We derive sharp upper bounds for eigenvalues of the Laplacian un- der Neumann boundary conditions on convex domains with given diameter in Euclidean space. We use the Brunn-Minkowski theorem in order to reduce the problem to a question about eigenvalues of certain classes of Sturm-Liouville problems.
View
On upper bounds for high order neumann eigenvalues of convex domains in euclidean space
Article
Jan 1999
Pawel Kröger
We derive sharp upper bounds for eigenvalues of the Laplacian under Neumann boundary conditions on convex domains with given diameter in Euclidean space. We use the Brunn-Minkowski theorem in order to reduce the problem to a question about eigenvalues of certain classes of Sturm-Liouville problems.
View
On the Ranges of Eigenfunctions on Compact Manifolds
Article
Nov 1998
Pawel Kröger
The aim of this note is to give a sharp upper bound on the ratio [formula] where φ is a nonconstant eigenfunction for the Laplace–Beltrami operator on a connected compact Riemannian manifold without boundary. This ratio is always positive, since maxφ>0 and minφ<0 for every nonconstant eigenfunction. We assume that maxφ≥−minφ, in order to simplify...
View
Isoperimetric-type bounds for solutions of the heat equation
Article
Mar 1997
Rodrigo Banuelos
Pawel Kröger
View
On explicit bounds for the spectral gap on compact manifolds
Article
Jan 1997
Pawel Kröger
View
On the ground state eigenfunction of a convex domain in Euclidean space
Article
Feb 1996
Pawel Kröger
We study the first eigenfunction f1 of the Dirichlet Laplacian on a convex domain in Euclidean space. Elementary properties of Bessel functions yield that $$\left\| {\phi _1 } \right\|_\infty /\left\| {\phi _1 } \right\|_2 \to \infty$$ if D is a sector in Euclidean plane with area 1 and the angle tends to 0. We aim to characterize those domains D...
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A counterexample in parabolic potential theory
Article
Dec 1995
Pawel Kröger
View
Estimates for Sums of Eigenvalues of the Laplacian
Article
Nov 1994
Pawel Kröger
The aim of this paper is to give bounds for the eigenvalues of the Laplacian on a domain in Euclidean space and on a compact Riemannian manifold. First, we consider the eigenvalue problem for the Laplacian on a bounded domain in Euclidean space under Dirichlet and Neumann boundary conditions. Our method for obtaining an upper bound for sums of eige...
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Regularity conditions on parabolic measures
Article
Oct 1994
Pawel Kröger
Without Abstract
View
H�lder continuity of normalized solutions of the Schr�dinger equation
Article
Jan 1993
Pawel Kröger
Karl-Theodor Sturm
Definition 1. Assume that V~ L~~ A function u is called local weak solution of the Schr6dinger equation (-�89 V)u = 0 on an open subset D c R d if u ~ L]~162 V. u ~ L~~ and 1 f u. ~r f. v.u. r = 0 v~, ~ ~e~mp(O). 2D o
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ON The spectral gap for compact manifolds
Article
Sep 1992
Pawel Kröger
View
Upper Bounds for the Neumann Eigenvalues on a Bounded Domain in Euclidean Space
Article
Jun 1992
Pawel Kröger
Let μk be the the kth eigenvalue for the Neumann boundary value problem with respect to the Laplace operator on a bounded domain Ω with piecewise smooth boundary in Rn. Weyl's asymptotic formula states that . We aim to give an upper bound for partial sums ∑jk = 1 μj of eigenvalues. Our bound depends only on the volume of Ω and is to some extent asy...
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A Counterexample for $L^1$-Estimates for Parabolic Differential Equations
Article
Sep 1992
Pawel Kröger
We show that the Dini (1) continuity of the coefficients of a linear parabolic differential operator in non-divergence form is in some sense the weakest condition such that the solutions of the corresponding initial value problem satisfy an L 1 -estimate. Here a function is called Dini (α) continuous for a positive number α if the modulus of contin...
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Comparison theorems for diffusion processes
Article
Oct 1990
Pawel Kröger
We prove comparison theorems for diffusion processes onR d. From these theorems we derive lower and upper bounds for the transition probabilities of a diffusion process. In contrast to the known estimates for fundamental solutions of parabolic equations our bounds do not depend on the moduli of continuity of the coefficients of the differential ope...
View
Harmonic spaces associated with parabolic and elliptic differential operators
Article
Nov 1989
Pawel Kröger
View
Comparaison de diffusions. (Comparison of diffusion processes)
editArticle
Jan 1987
Pawel Kröger
View
Comparaison de diffusions. (Comparison of diffusion processes)
January 1987
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Derivationen in L (D)
edithttps://www.researchgate.net/publication/266955156_Derivationen_in_L_D
Article
Jan 1975
Pawel Kröger
View
Derivationen in L (D)
January 1975
Wissenschaftliche Zeitschrift der Karl-Marx-Universität Leipzig.
Mathematisch-naturwissenschaftliche Reihe 24
Estimates for eigenvalues of the Laplacian
Article
Pawel Kröger
G. Pólya conjectured in 1954 that the first term in Weyl’s asymptotic formula is a lower bound for the Dirichlet eigenvalues and an upper bound for the Neumann eigenvalues of the Laplacian on a domain in Euclidean space. Although Pólya succeeded in proving his conjecture for a special class of domains with the property that the Euclidean space can...
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Regularity properties of parabolic measures
Article
Pawel Kröger
View
Vergleichssätze für Diffusionsprozesse. (Comparison theorems for diffusion processes)
editVergleichssätze für Diffusionsprozesse. (Comparison theorems for diffusion processes)
Article
Pawel Kröger
Research related information
edithttps://sites.google.com/site/pawelkroeger
Research related information
email: [email protected]
Publications: scholar.google MathSciNet Scopus zbMATH orcid.org
The best constant in the Poincaré inequality on a compact Riemannian manifold and related topics
An estimate under a lower bound on the Ricci curvature and an upper bound for the diameter was obtained in P. Kröger "On the spectral gap for compact manifolds",
J. Differ. Geom. 36, 315--330 (1992), Spectral gap compact manifolds.pdf . The final publication is available at proyecteuclid.org .
That estimate is sharp for all manifolds of a given dimension that satisfy the above bounds. The proof is based on the maximum principle technique.
The main problem in earlier works by S. T. Yau, P. Li and S. T. Yau, J. Q. Zhong and H. C. Yang was that the ranges of the eigenfunctions are not symmetric with respect
to the origin. That motivates our paper "On the ranges of eigenfunctions on compact manifolds", Bull. London Math. Soc. 30, 651--656 (1998)
Ranges of Eigenfunctions.pdf Ranges of Eigenfunctions2.pdf where sharp bounds for the quotients max u/(-min u) for eigenfunctions u are obtained.
Estimates for sums of eigenvalues of the Laplacian
Our estimates are based on the variational characterization of eigenvalues as applied by P. Li and S. T. Yau to the task of
estimating Dirichlet eigenvalues. We applied similar techniques to Neumann eigenvalues in P. Kröger "Upper bounds for
the Neumann eigenvalues on a bounded domain in Euclidean space", J. Funct. Anal. 106, 353--357 (1992)
https://doi.org/10.1016/0022-1236(92)90052-K Upper bounds Neumann eigenvalues.pdf .
Our aim in P. Kröger "Estimates for sums of eigenvalues of the Laplacian", J. Funct. Anal. 126, 217--227 (1994)
https://doi.org/10.1006/jfan.1994.1146 Sums of eigenvalues.pdf was to complement the previous bounds by upper bounds
for Dirichlet eigenvalues and lower bounds for Neumann eigenvalues.
Upper bounds for Neumann eigenvalues of convex domains in Euclideans space
We improve the bounds obtained earlier by S. Y. Cheng to sharp bounds for convex domains with given diameter in P. Kröger
"On upper bounds for high order Neumann eigenvalues of convex domains in Euclidean space", Proc. Amer. Math. Soc. 127,
1665--1669 (1999) Upper bounds Neumann eigenvalues convex.pdf .
A second-order differential inequality on area growth
We extend Günther's volume comparison theorem in order to obtain a second-order differential inequality.
Günther's theorem can be obtained from our theorem by integration.
P. Kröger "An extension of Günther's volume comparison theorem", Math. Ann. 329, 593--596 (2004)
The final publication is available at Springer via: https://doi.org/10.1007/s00208-004-0520-7 Günther's Volume Comparison.pdf.
Gradient estimates for solutions of the Schrödinger equation and the heat equation
Both articles are joint work with R. Bañuelos (Purdue) and are based on the maximum principle techique: R. Bañuelos, P. Kröger
"Gradient estimates for the ground state Schrödinger eigenfunction and applications", Comm. Math. Phys. 224, 545--550 (2001) with link to final
publication Springer https://doi.org/10.1007/s002200100551 Gradient estimates.pdf and "Isometric-type bounds for solutions of the heat equation",
Indiana Univ. Math. J. 46, 83--91 (1997) with link to Indiana Univ. Math. J.: Isoperimetric Bounds.
Potential theory, regularity of solutions of elliptic and parabolic equations
The papers P. Kröger "Regular Boundary Points and Exit Distributions for Parabolic Differential Operators", Potential Analysis 49, 203--207 (2018) with
Springer link to .pdf: Regular Boundary Points.pdf , P. Kröger "A counterexample in parabolic potential theory", Mathematika 42, 392--396 (1995)
Counterexample parabolic potential.pdf and P. Kröger "Harmonic spaces associated with parabolic and elliptic differential operators", Math. Ann. (1989)
available at Springer via: https://doi.org/10.1007/BF01455064 Springer link: Harmonic Spaces Parabolic Elliptic Operators deal with problems from potential theory.
The article with K.-Th. Sturm (Bonn) is concerned with Hölder continuity of solutions of the Schrödinger equation. It turns out that
quotients of solutions are more regular that the solutions themselves: P. Kröger, K.-Th. Sturm "Hölder continuity of normalized solutions of Schrödinger equations",
Math. Ann. 297, 663--670 (1993) and final publication available at Springer via: https://doi.org/10.1007/BF01459522 Hölder continuity Schrödinger.pdf.
The articles P. Kröger, "Regularity conditions on parabolic measures", Ark. Mat. 32, 373--391 (1994) https://doi.org/10.1007/BF02559577
Regularity parabolic measures.pdf and P. Kröger, "A counterexample for L1-estimates for parabolic differential equations", Z. Anal. Anwend. 11, 401--406 (1992)
Counterexample L^1 estimates.pdf deal with singular solutions.
Main Papers (with links)
Regular Boundary Points and Exit Distributions for Parabolic Differential Operators. Potential Analysis 49, 203--207 (2018)
Springer link to .pdf: Regular Boundary Points
An extension of Günther's volume comparison theorem. Math. Ann. 329, 593--596 (2004)
The final publication is available at Springer via: https://doi.org/10.1007/s00208-004-0520-7 Günther's Volume Comparison.pdf
(with R. Bañuelos) Gradient estimates for the ground state Schrödinger eigenfunction and applications.
Comm. Math. Phys. 224, 545--550 (2001) The final publication is available at Springer via: https://doi.org/10.1007/s002200100551 Gradient estimates.pdf
(with E. Harrell and K. Kurata) On the placement of an obstacle or a well so as to optimize the fundamental eigenvalue.
SIAM J. Math. Anal. 33, 240--259 (2001) https://doi.org/10.1137/S0036141099357574 Placement Obstacle Eigenvalue.pdf
On upper bounds for high order Neumann eigenvalues of convex domains in Euclidean space.
Proc. Amer. Math. Soc. 127, 1665--1669 (1999) https://doi.org/10.1090/S0002-9939-99-04804-2 Upper bounds Neumann eigenvalues convex.pdf
On the ranges of eigenfunctions on compact manifolds. Bull. London Math. Soc. 30, 651--656 (1998) Ranges of Eigenfunctions.pdf Ranges of Eigenfunctions2.pdf
On explicit bounds for the spectral gap on compact manifolds. Soochow J. Math. 23, 339--344 (1997) Explicit bounds spectral gap.pdf
(with Bañuelos, R.) Isometric-type bounds for solutions of the heat equation. Indiana Univ. Math. J. 46, 83--91 (1997)
Link to Indiana Univ. Math. J.: Isoperimetric Bounds
On the ground state eigenfunction of a convex domain in Euclidean space. Potential Anal. 5, 103--108 (1996)
The final publication is available at Springer via: https://doi.org/10.1007/BF00276699 Ground state convex domain.pdf
Estimates for eigenvalues of the Laplacian. In: Proc. of the ICPT 94. Walther de Gruyter.
A counterexample in parabolic potential theory. Mathematika 42, 392--396 (1995) https://doi.org/10.1112/S0025579300014662
Counterexample parabolic potential.pdf
Regularity conditions on parabolic measures. Ark. Mat. 32, 373--391 (1994) https://doi.org/10.1007/BF02559577 Regularity parabolic measures.pdf
Estimates for sums of eigenvalues of the Laplacian. J. Funct. Anal. 126, 217--227 (1994) https://doi.org/10.1006/jfan.1994.1146 Sums of eigenvalues.pdf
(with Sturm, K.-Th.) Hölder continuity of normalized solutions of Schrödinger equations. Math. Ann. 297, 663--670 (1993)
The final publication is available at Springer via: https://doi.org/10.1007/BF01459522 Hölder continuity Schrödinger.pdf
On the spectral gap for compact manifolds. J. Differ. Geom. 36, 315--330 (1992) Spectral gap compact manifolds.pdf, final publication available at proyecteuclid.org
Upper bounds for the Neumann eigenvalues on a bounded domain in Euclidean space. J. Funct. Anal. 106, 353--357 (1992)
https://doi.org/10.1016/0022-1236(92)90052-K Upper bounds Neumann eigenvalues.pdf
A counterexample for L1-estimates for parabolic differential equations. Z. Anal. Anwend. 11, 401--406 (1992) Counterexample L^1 estimates.pdf
Harmonic spaces associated with parabolic and elliptic differential operators, Math. Ann. 285 (3), 393-403 (1989)
The final publication is available at Springer via: https://doi.org/10.1007/BF01455064, Springer link: Harmonic Spaces Parabolic Elliptic Operators.
Other Web points of interest: ResearchGate Mathematics Genealogy Project IMO official 1972 IMO official 1973
Zeitschrift Alpha
editalpha (vollständiger Titel alpha – Mathematische Schülerzeitschrift) war eine vom Verlag Volk und Wissen in der DDR herausgegebene mathematische Zeitschrift für Schüler. Ihre erste Ausgabe erschien 1967. Es gab sechs Hefte pro Jahr. Chefredakteur im über fünfzehnköpfigen Redaktionskollegium war während der ersten zwanzig Jahre der Leipziger Mathematiklehrer Johannes Lehmann (1922–1995). Die Auflagenhöhe betrug zeitweilig knapp 100.000.[1]
Die Artikel in den 32-seitigen Heften, die über den Unterrichtsstoff hinausgingen und das Interesse an der Mathematik wecken sollten, stammten von Lehrern, Hochschullehrern und Wissenschaftlern und behandelten mathematische Methoden und Aufgaben, naturwissenschaftliche Themen mit mathematischem Hintergrund, Biographien usw. Sie waren jeweils gekennzeichnet, ab welcher Klassenstufe sie geeignet waren.
Zusätzlich gab es einige Seiten zum alpha-Wettbewerb. Pro Klassenstufe wurden etwa sechs Aufgaben aus den Bereichen Mathematik, Physik und Chemie veröffentlicht. Teilnehmer konnten Aufgaben ihrer Klassenstufe oder höherer Klassenstufen lösen. Erwachsene lösten Aufgaben der Klassenstufe 11/12. Eingesandte Lösungen wurden mit „sehr gut gelöst“, „gut gelöst“ oder „gelöst“ bewertet. Zum Wettbewerbsende wurden alle Lösungskarten eingesandt, um das alpha-Abzeichen in Gold, Silber oder Bronze zu erhalten. In der Zeitschrift erschienen Listen, über wie viele Jahre ein Schüler bereits erfolgreich am Wettbewerb teilgenommen hatte.