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Heat Kernel and Analysis on Manifolds (Paperback, New ed.)
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Heat Kernel and Analysis on Manifolds (Paperback, New ed.)
Series: AMS/IP Studies in Advanced Mathematics
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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
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
this 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. Titles in this series are
co-published with International Press, Cambridge, MA, USA.
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