AMS/IP studies in advanced mathematics· 2012
Heat Kernel and Analysis on Manifolds
- 526citations
- 2012year
Short summary
This paper provides a comprehensive reference on the heat kernel and related analytical techniques on manifolds, covering fundamental properties, estimates, and applications.
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Key points
- Covers the Laplace operator and heat equation in $\mathbb{R}^n$ and on Riemannian manifolds.
- Explores fundamental concepts like the weak maximum principle and regularity theory.
- Details various forms of Gaussian estimates for the heat kernel.
- Discusses Green functions, Green operators, and spectral properties.
- Includes ultracontractive estimates and their relation to eigenvalues.
AI-generated from the title and abstract; the full text is not read.
Abstract
Laplace operator and the heat equation in $\mathbb{R}^n$ Function spaces in $\mathbb{R}^n$ Laplace operator on a Riemannian manifold Laplace operator and heat equation in $L^{2}(M)$ Weak maximum principle and related topics Regularity theory in $\mathbb{R}^n$ 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 Reference material Bibliography Some notation Index
The authors' abstract, as published at the source. AMS/IP studies in advanced mathematics, 2012 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics