Isoperimetric inequalities: differential geometric and analytic perspectives
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2001
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
145 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 268 S. graph. Darst. |
| ISBN: | 0521802679 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface page ix
I Introduction 1
1.1 The Isoperimetric Problem 1
1.2 The Isoperimetric Inequality in the Plane 4
1.3 Preliminaries 13
1.4 Bibliographic Notes 28
II Differential Geometric Methods 30
II. 1 The C2 Uniqueness Theory 30
11.2 The C Isoperimetric Inequality 44
11.3 Bibliographic Notes 51
III Minkowski Area and Perimeter 52
III. 1 The Hausdorff Metric on Compacta 53
111.2 Minkowski Area and Steiner Symmetrization 58
111.3 Application: The Faber Krahn Inequality 78
111.4 Perimeter 81
111.5 Bibliographic Notes 99
IV Hausdorff Measure and Perimeter 100
IV. 1 Hausdorff Measure 100
IV.2 The Area Formula for Lipschitz Maps 110
IV.3 Bibliographic Notes 116
V Isoperimetric Constants 117
V. 1 Riemannian Geometric Preliminaries 118
V.2 Isoperimetric Constants 127
V.3 Discretizations and Isoperimetric Inequalities 139
V.4 Bibliographic Notes 155
vii
viii Contents
VI Analytic Isoperimetric Inequalities 157
VI. 1 L2 Sobolev Inequalities 157
VI.2 The Compact Case 161
VI.3 Faber Krahn Inequalities 165
VI.4 The Federer Fleming Theorem: The Discrete Case 170
VI.5 Sobolev Inequalities and Discretizations 174
VI.6 Bibliographic Notes 183
VII Laplace and Heat Operators 185
VII. 1 Self adjoint Operators and Their Semigroups 185
VII.2 TheLaplacian 192
VII.3 The Heat Equation and Its Kernels 201
VII.4 The Action of the Heat Semigroup 216
VII.5 Simplest Examples 222
VII.6 Bibliographic Notes 224
VIII Large Time Heat Diffusion 225
VHI.l The Main Problem 226
VIII.2 The Nash Approach 234
VIII.3 The Varopoulos Approach 236
VIII.4 Coulhon s Modified Sobolev Inequality 240
VIII.5 The Denouement: Geometric Applications 243
j VIII.6 Epilogue: The Faber Krahn Method 249
VIII.7 Bibliographic Notes 253
Bibliography 255
Author Index 263
Subject Index 265
|
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| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T18:55:12Z |
| institution | BVB |
| isbn | 0521802679 |
| language | English |
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| physical | XII, 268 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| publisher | Cambridge Univ. Press |
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| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Chavel, Isaac Verfasser (DE-588)110636805 aut Isoperimetric inequalities differential geometric and analytic perspectives Isaac Chavel 1. publ. Cambridge Cambridge Univ. Press 2001 XII, 268 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 145 Isoperimetrische Ungleichung Isoperimetrische Ungleichung (DE-588)4162544-4 gnd rswk-swf Isoperimetrische Ungleichung (DE-588)4162544-4 s DE-604 Cambridge tracts in mathematics 145 (DE-604)BV000000001 145 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009556377&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chavel, Isaac Isoperimetric inequalities differential geometric and analytic perspectives Cambridge tracts in mathematics Isoperimetrische Ungleichung Isoperimetrische Ungleichung (DE-588)4162544-4 gnd |
| subject_GND | (DE-588)4162544-4 |
| title | Isoperimetric inequalities differential geometric and analytic perspectives |
| title_auth | Isoperimetric inequalities differential geometric and analytic perspectives |
| title_exact_search | Isoperimetric inequalities differential geometric and analytic perspectives |
| title_full | Isoperimetric inequalities differential geometric and analytic perspectives Isaac Chavel |
| title_fullStr | Isoperimetric inequalities differential geometric and analytic perspectives Isaac Chavel |
| title_full_unstemmed | Isoperimetric inequalities differential geometric and analytic perspectives Isaac Chavel |
| title_short | Isoperimetric inequalities |
| title_sort | isoperimetric inequalities differential geometric and analytic perspectives |
| title_sub | differential geometric and analytic perspectives |
| topic | Isoperimetrische Ungleichung Isoperimetrische Ungleichung (DE-588)4162544-4 gnd |
| topic_facet | Isoperimetrische Ungleichung |
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