Geometric analysis / Peter Li.

Includes bibliographical references and index.

The aim of this graduate-level text is to equip the reader with the basic tools and techniques needed for research in various areas of geometric analysis. Throughout, the main theme is to present the interaction of partial differential equations and differential geometry. More specifically, emphasis is placed on how the behavior of the solutions of a PDE is affected by the geometry of the underlying manifold and vice versa. For efficiency the author mainly restricts himself to the linear theory and only a rudimentary background in Riemannian geometry and partial differential equations is assumed. Originating from the author's own lectures, this book is an ideal introduction for graduate students, as well as a useful reference for experts in the field.

Cover; CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS 134; Geometric Analysis; CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS; Title; Copyright; Dedication; Contents; Preface; 1 First and second variational formulas for area; 2 Volume comparison theorem; 3 Bochner-Weitzenböck formulas; 4 Laplacian comparison theorem; 5 Poincaré inequality and the first eigenvalue; 6 Gradient estimate and Harnack inequality; 7 Mean value inequality; 8 Reilly's formula and applications; 9 Isoperimetric inequalities and Sobolev inequalities; 10 The heat equation; 11 Properties and estimates of the heat kernel.

Print version record.

English.

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