No cover image available.

AMS/IP Studies in Advanced Mathematics

Volume 47

Heat Kernel and Analysis on Manifolds

Alexander Grigor’yan (Bielefeld University)

Original Publication: 1 November 2009

Publisher: American Mathematical Society / International Press

Language: English

Hardcover

500 pages

List Price: $119.00

Description

The heat kernel has long been an essential tool in both classical and modern mathematics, but has become especially important in geometric analysis as a result of major innovations beginning in the 1970s. The methods based on heat kernels have been used in the areas as diverse as analysis, geometry, and probability, as well as in physics. This book is a comprehensive introduction to heat kernel techniques in the setting of Riemannian manifolds, which inevitably involves analysis of the Laplace-Beltrami operator and the associated heat equation.

The first ten chapters cover the foundations of the subject, while later chapters deal with more advanced results involving the heat kernel in a variety of settings. The exposition starts with an elementary introduction to Riemannian geometry, proceeds with a thorough study of the spectral-theoretic, Markovian, and smoothness properties of the Laplace and heat equations on Riemannian manifolds, and concludes with Gaussian estimates of heat kernels.

Grigor’yan has written the book with the student in mind, in particular by including over 400 exercises. The text will serve as a bridge between basic results and current research.

This volume is part of the AMS/IP Studies in Advanced Mathematics book series.

Publications

Pub. Date

ISBN-13

ISBN-10

Medium

Binding

Size, Etc.

Status

List Price

2015 Jan

9780821893937

0821893939

Print

paperback

Out of Print

2009 Nov

9780821849354

0821849352

Print

hardcover

In Print

US$119.00