Eigenvalues in Riemannian geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Orlando [u.a.]
Acad. Press
2004
|
| Ausgabe: | Transferred to digital print. |
| Schriftenreihe: | Pure and applied mathematics
115 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 362 S. |
| ISBN: | 0121706400 |
Internformat
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| 100 | 1 | |a Chavel, Isaac |e Verfasser |0 (DE-588)110636805 |4 aut | |
| 245 | 1 | 0 | |a Eigenvalues in Riemannian geometry |c Isaac Chavel. With a chapter by Burton Randol. With appendix by Jozef Dodziuk |
| 250 | |a Transferred to digital print. | ||
| 264 | 1 | |a Orlando [u.a.] |b Acad. Press |c 2004 | |
| 300 | |a XIV, 362 S. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface
xi
CHAPTER I
The Lapladan
1.
Definitions and Preliminaries
1
2.
Green s Formulas
5
3.
Basic Facts for Eigenvalue Problems
7
4.
The Wave and Heat Equations
11
5.
Rayleigh and
Max-Min
Methods
13
CHAPTER II
The Basic Examples
1.
Some Generalities
26
2.
Tori
28
3.
Weyľs
Formula for Bounded Domains in R
31
4.
Spheres and Real
Projective
Spaces
33
5.
Disks in Constant Curvature Space Forms
36
CHAPTER HI
λι
and Curvature
1.
Geodesies and Curvature
55
2.
Comparison Theorems for Sectional Curvature Bounded
from Above
67
3.
Comparison Theorems for
Ricci
Curvature Bounded from
Below
71
4.
Obata and Toponogov Theorems
82
CHAPTER IV
Isoperimetric Inequalities
1.
The Co-Area Formula
85
2.
The Faber-Krahn Inequality
86
viii Contents
3.
The Cheeger, Sobolev, and Isoperimetric Constants
95
4.
The Sobolev Constant and Eigenvalue, Eigenfunction, Esti¬
mates
99
5.
The Constants and Estimates for the Closed Eigenvalue
Problem
109
CHAPTER V
Eigenvalues and the Kinematic Measure
1.
The Analytic Inequality
113
2.
M. Berger s Isoembolic Inequality
117
3.
Cheeger and Isoperimetric Constants, and the Kinematic
Measure
124
CHAPTER VI
The Heat Kernel for Compact Manifolds
1.
Duhamel s Principle and Its Consequences
136
2.
The Heat Equation on R
142
3.
The Minakshisundaram-Pleijel Recursion Formulas
148
4.
Existence of the Heat Kernel
151
CHAPTER
VII
The Dirichlet Heat Kernel for Regular Domains
1.
Preliminaries
159
2.
The Dirichlet Heat Kernel for Regular Domains
161
3.
Duhamel s Principle
164
CHAPTER
VIII
The Heat Kernel for Noncompact Manifolds
1.
The Maximum Principle, and Uniqueness Theorems, for the
Heat Operator
180
2.
The Heat Kernel for Noncompact Manifolds
187
3.
Comparison Theorems for Heat Kernels
192
4.
Upper Bounds for the Heat Kernel
196
CHAPTER IX
Topological Perturbations with Negligible Effect
1.
Statement and Discussion of the Results
209
2.
Proof of Theorems
1-6 216
Contents
IX
3.
Using Rayleigh s Characterization of Eigenvalues
228
4.
The Mathematics of Crashed Ice
233
CHAPTER X
Surfaces of Constant Negative Curvature
1.
Geometry of the Hyperbolic Plane
239
2.
The Heat Kernel of the Hyperbolic Plane
242
3. Löbell
Surfaces and the Estimates of P.
Buser 246
4.
Low Eigenvalues and Short Geodesies
254
5.
The Upper Half-Space Model of Hyperbolic Space
262
CHAPTER XI
The Selberg Trace Formula by Burton Randoi
1.
Preliminaries
266
2.
The
Pretrace
Formula
271
3.
Applications of the
Pretrace
Formula
278
4.
The Trace Formula
288
5.
Applications of the Trace Formula
293
6.
Concluding Remarks
302
CHAPTER
XII
Miscellanea
1.
Volumes of Disks and Spheres
303
2.
The Fourier Transform
304
3.
The
Poisson
Summation Formula
306
4.
The Fourier Transform and the Heat Equation
307
5.
Eigenfunctions on Spheres and Hyperbolic Space
308
6.
Minimal Submanifolds of Euclidean Spaces and Spheres
309
7.
Normalization of Geometric Data
314
8.
Geodesic Coordinates
316
9.
The Levy-Gromov Isoperimetric Inequality
322
10.
Heat Conduction on the Euclidean Upper Half-Space
325
11.
The Maximum Principle for the Laplacian
329
12.
Recent Progress on Eigenvalue and Heat Kernel Estimates
330
APPENDIX
Laplacian on Forms by
Jozef Dodziuk
334
Bibliography
345
Index
359
|
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| classification_rvk | SK 370 SK 540 |
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| discipline | Mathematik |
| edition | Transferred to digital print. |
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| id | DE-604.BV020014841 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:10:52Z |
| institution | BVB |
| isbn | 0121706400 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013336323 |
| oclc_num | 179879962 |
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| owner | DE-19 DE-BY-UBM DE-355 DE-BY-UBR |
| owner_facet | DE-19 DE-BY-UBM DE-355 DE-BY-UBR |
| physical | XIV, 362 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Acad. Press |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Chavel, Isaac Verfasser (DE-588)110636805 aut Eigenvalues in Riemannian geometry Isaac Chavel. With a chapter by Burton Randol. With appendix by Jozef Dodziuk Transferred to digital print. Orlando [u.a.] Acad. Press 2004 XIV, 362 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 115 Eigenwert (DE-588)4151200-5 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Laplace-Operator (DE-588)4166772-4 gnd rswk-swf Eigenwert (DE-588)4151200-5 s Riemannsche Geometrie (DE-588)4128462-8 s DE-604 Laplace-Operator (DE-588)4166772-4 s Pure and applied mathematics 115 (DE-604)BV010177228 115 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013336323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chavel, Isaac Eigenvalues in Riemannian geometry Pure and applied mathematics Eigenwert (DE-588)4151200-5 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd Laplace-Operator (DE-588)4166772-4 gnd |
| subject_GND | (DE-588)4151200-5 (DE-588)4128462-8 (DE-588)4166772-4 |
| title | Eigenvalues in Riemannian geometry |
| title_auth | Eigenvalues in Riemannian geometry |
| title_exact_search | Eigenvalues in Riemannian geometry |
| title_full | Eigenvalues in Riemannian geometry Isaac Chavel. With a chapter by Burton Randol. With appendix by Jozef Dodziuk |
| title_fullStr | Eigenvalues in Riemannian geometry Isaac Chavel. With a chapter by Burton Randol. With appendix by Jozef Dodziuk |
| title_full_unstemmed | Eigenvalues in Riemannian geometry Isaac Chavel. With a chapter by Burton Randol. With appendix by Jozef Dodziuk |
| title_short | Eigenvalues in Riemannian geometry |
| title_sort | eigenvalues in riemannian geometry |
| topic | Eigenwert (DE-588)4151200-5 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd Laplace-Operator (DE-588)4166772-4 gnd |
| topic_facet | Eigenwert Riemannsche Geometrie Laplace-Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013336323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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