Extremal metrics for eigenvalues of the Laplace-Beltrami operator on surfaces

被引：7

作者：

Penskoi, A. V. ^{[1
,2
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow, Russia

[2] Independent Univ Moscow, Moscow, Russia

来源：

RUSSIAN MATHEMATICAL SURVEYS | 2013年 / 68卷 / 06期

关键词：

geometric optimisation of eigenvalues; extremal metrics; minimal; surfaces in spheres; ISOPERIMETRIC INEQUALITY; SPECTRAL PROPERTIES; 1ST EIGENVALUE; MINIMAL IMMERSIONS; UPPER-BOUNDS; TORI; MULTIPLICITY; MANIFOLDS;

D O I：

10.1070/RM2013v068n06ABEH004870

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Known results on geometric optimisation of eigenvalues of the Laplace operator are briefly reviewed, and a more detailed survey of recent results in the theory of extremal metrics on surfaces is presented.

引用

页码：1073 / 1130

页数：58

共 50 条

[11] Momentum tunneling between tori and the splitting of eigenvalues of the laplace-beltrami operator on liouville surfaces
Dobrokhotov S.Y.U.
Mathematical Physics, Analysis and Geometry, 1999, 2 (2) : 141 - 177
[12] Heat Kernel Laplace-Beltrami Operator on Digital Surfaces
Caissard, Thomas
Coeurjolly, David
Lachaud, Jacques-Olivier
Roussillon, Tristan
DISCRETE GEOMETRY FOR COMPUTER IMAGERY, DGCI 2017, 2017, 10502 : 241 - 253
[13] On approximation of the Laplace-Beltrami operator and the Willmore energy of surfaces
Hildebrandt, Klaus
Polthier, Konrad
COMPUTER GRAPHICS FORUM, 2011, 30 (05) : 1513 - 1520
[14] Simplification of the Laplace-Beltrami operator
Hashiguchi, H
Nakagawa, S
Niki, N
MATHEMATICS AND COMPUTERS IN SIMULATION, 2000, 51 (05) : 489 - 496
[15] The Hyperbolic Laplace-Beltrami Operator
Fraczek, Markus Szymon
SELBERG ZETA FUNCTIONS AND TRANSFER OPERATORS: AN EXPERIMENTAL APPROACH TO SINGULAR PERTURBATIONS, 2017, 2139 : 87 - 127
[16] A sharp estimate for Neumann eigenvalues of the Laplace-Beltrami operator for domains in a hemisphere
Benguria, Rafael D.
Brandolini, Barbara
Chiacchio, Francesco
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2020, 22 (03)
[17] MULTIPLICATIVE RENORMALIZABILITY AND THE LAPLACE-BELTRAMI OPERATOR
OLIVIER, D
VALENT, G
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 1991, 6 (06): : 955 - 976
[18] The Berezin transform and Laplace-Beltrami operator
Li, Bo
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 327 (02) : 1155 - 1166
[19] THE GAPS IN THE SPECTRUM OF THE LAPLACE-BELTRAMI OPERATOR
LEE, JM
HOUSTON JOURNAL OF MATHEMATICS, 1991, 17 (01): : 1 - 24
[20] SPECTRAL RESONANCES FOR THE LAPLACE-BELTRAMI OPERATOR
DEBIEVRE, S
HISLOP, PD
ANNALES DE L INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE, 1988, 48 (02): : 105 - 145

← 1 2 3 4 5 →