Isoperimetric Inequalities

Author: Isaac Chavel
Publisher: Cambridge University Press
ISBN: 0521802679
Release Date: 2001-07-23
Genre: Mathematics

This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject.

Heat Kernel and Analysis on Manifolds

Author: Alexander Grigoryan
Publisher: American Mathematical Soc.
ISBN: 9780821849354
Release Date: 2009
Genre: Mathematics

"This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincaré Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and p -Laplace operators, heat kernel and spherical inversion on SL 2 (C) , random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs."--Publisher's website.

Mean Curvature Flow and Isoperimetric Inequalities

Author: Manuel Ritoré
Publisher: Springer Science & Business Media
ISBN: 9783034602136
Release Date: 2010-01-01
Genre: Mathematics

Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.

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Author:
Publisher:
ISBN: UOM:39015072701728
Release Date: 2008
Genre: Mathematics


Variational Principles for Discrete Surfaces

Author: Junei Dai
Publisher: International Pressof Boston Incorporated
ISBN: 1571461728
Release Date: 2008
Genre: Mathematics

This new volume introduces readers to some of the current topics of research in the geometry of polyhedral surfaces, with applications to computer graphics. The main feature of the volume is a systematic introduction to the geometry of polyhedral surfaces based on the variational principle. The authors focus on using analytic methods in the study of some of the fundamental results and problems of polyhedral geometry: for instance, the Cauchy rigidity theorem, Thurston's circle packing theorem, rigidity of circle packing theorems, and Colin de Verdiere's variational principle. The present book is the first complete treatment of the vast, and expansively developed, field of polyhedral geometry.

Riemannian Geometry

Author: Isaac Chavel
Publisher:
ISBN: 0521432014
Release Date: 1993
Genre: Mathematics

This book provides an introduction to Riemannian geometry, the geometry of curved spaces. Its main theme is the effect of the curvature of these spaces on the usual notions of geometry - distances, areas, and volumes - and on those new notions and ideas motivated by curvature itself. Among the more specialized classical topics in a new setting are volume-comparison theorems, and isoperimetric inequalities - the interplay of curvature with volume of sets and the areas of their boundaries. Completely new themes created by curvature include the interaction of microscopic behavior of the geometry with the macroscopic structure of the space. After considering those topics which would form the core of an introductory course, the book emphasizes more specialized topics, here treated in book form for the first time. Also featured is a nontraditional Notes and Exercises section for each chapter, to develop and enrich the readers appetite for and appreciation of the subject.

Author:
Publisher:
ISBN: UOM:39015085197674
Release Date: 2008
Genre: Mathematics


Forthcoming Books

Author: Rose Arny
Publisher:
ISBN: UOM:39015046820406
Release Date: 2001-08
Genre: American literature


Books in Print

Author: R.R. Bowker Company
Publisher:
ISBN: UOM:39015054035236
Release Date: 2003-09
Genre: American literature

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.