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Heat Kernel and Analysis on Manifolds

✍ Scribed by Alexander Grigor’yan

Publisher
AMS
Year
2009
Tongue
English
Leaves
504
Series
AMS/IP Studies in Advanced Mathematics 47
Category
Library
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✦ Table of Contents

Cover
Title page
Dedication
Contents
Preface
Laplace operator and the heat equation in ℝⁿ
Function spaces in ℝⁿ
Laplace operator on a Riemannian manifold
Laplace operator and heat equation in 𝐿²(𝑀)
Weak maximum principle and related topics
Regularity theory in ℝⁿ
The heat kernel on a manifold
Positive solutions
Heat kernel as a fundamental solution
Spectral properties
Distance function and completeness
Gaussian estimates in the integrated form
Green function and Green operator
Ultracontractive estimates and eigenvalues
Pointwise Gaussian estimates I
Pointwise Gaussian estimates II
Appendix A. Reference material
Bibliography
Some notation
Index
Back Cover

✦ Subjects

Global analysis

πŸ“œ SIMILAR VOLUMES

Heat kernel and analysis on manifolds
πŸ“ Heat kernel and analysis on manifolds
✍ Grigor’yan A. πŸ“‚ Library πŸ“… 2009 πŸ› American Mathematical Society 🌐 English

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

Heat Kernel and Analysis on Manifolds
πŸ“ Heat Kernel and Analysis on Manifolds
✍ Alexander Grigor’yan πŸ“‚ Library πŸ“… 2009 πŸ› American Mathematical Society 🌐 English

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

Heat Kernel and Analysis on Manifolds
πŸ“ Heat Kernel and Analysis on Manifolds
✍ Alexander Grigor’yan πŸ“‚ Library πŸ“… 2009 πŸ› American Mathematical Society 🌐 English

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

Heat Kernel and Analysis on Manifolds
πŸ“ Heat Kernel and Analysis on Manifolds
✍ Alexander Grigor’yan πŸ“‚ Library πŸ“… 2009 πŸ› American Mathematical Society 🌐 English

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