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Isoperimetric Inequalities Differential Geometric and Analytic Perspectives

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ISBN-10: 1107402271

ISBN-13: 9781107402270

Edition: 2011

Authors: Isaac Chavel

List price: $68.95
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Book details

List price: $68.95
Copyright year: 2011
Publisher: Cambridge University Press
Publication date: 7/21/2011
Binding: Paperback
Pages: 282
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 0.946
Language: English

Introduction
The isoperimetric problem
The isoperimetric inequality in the plane
Preliminaries
Bibliographic notes
Differential Geometric Methods
The C2 uniqueness theory
The C1 isoperimetric inequality
Bibliographic notes
Minkowski Area and Perimeter
The Hausdorff metric on compacta
Minkowski area and Steiner symmetrization
Application: the Faber-Krahn inequality
Perimeter
Bibliographic notes
Hausdorff Measure and Perimeter
Hausdorff measure
The area formula for Lipschitz maps
Bibliographic notes
Isoperimetric Constants
Riemannian geometric preliminaries
Isoperimetric constants
Discretizations and isoperimetric inequalities
Bibliographic notes
Analytic Isoperimetric Inequalities
L2-Sobolev inequalities
The compact case
Faber-Kahn inequalities
The Federer-Fleming theorem: the discrete case
Sobolev inequalities and discretizations
Bibliographic notes
Laplace and Heat Operators
Self-adjoint operators and their semigroups
The Laplacian
The heat equation and its kernels
The action of the heat semigroup
Simplest examples
Bibliographic notes
Large-Time Heat Diffusion
The main problem
The Nash approach
The Varopoulos approach
Coulhon's modified Sobolev inequality
The denoument: geometric applications
Epilogue: the Faber-Kahn method
Bibliographic notes
Bibliography