Heat flow out of a compact manifold

DOI10.1007/s12220-014-9485-2zbMath1322.58017arXiv1306.6257OpenAlexW2033658702MaRDI QIDQ490762

Peter B. Gilkey, Michiel van den Berg

Publication date: 28 August 2015

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.6257

zbMATH Keywords

manifoldLaplace operatorheat flow

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Boundary value problems on manifolds (58J32) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (16)

Heat content estimates over sets of finite perimeter ⋮ On the heat content of a polygon ⋮ Heat content for convolution semigroups ⋮ Short-time heat content asymptotics via the wave and eikonal equations ⋮ First-order heat content asymptotics on \(\mathsf{RCD} (K, N)\) spaces ⋮ Heat content estimates for the fractional Schrödinger operator \((-\Delta)^{\frac{\alpha}{2}} + c1_{\Omega}\), \(c > 0\) ⋮ Heat flow from polygons ⋮ Hypoelliptic operators in geometry. Abstracts from the workshop held May 21--26, 2023 ⋮ Heat-content and diffusive leakage from material sets in the low-diffusivity limit ^* ⋮ Heat content in non-compact Riemannian manifolds ⋮ Heat content for stable processes in domains of \(\mathbb {R}^d\) ⋮ A note on the generalized heat content for L\'evy processes ⋮ Heat content and horizontal mean curvature on the Heisenberg group ⋮ Heat content with singular initial temperature and singular specific heat ⋮ Small time asymptotics of spectral heat contents for subordinate killed Brownian motions related to isotropic α‐stable processes ⋮ Uniform bounds for the heat content of open sets in Euclidean space

Uses Software

• Mathematica

Cites Work

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• Heat flow and perimeter in \(\mathbb{R}^m\)
• Neumann heat content asymptotics with singular initial temperature and singular specific heat
• Heat content asymptotics with singular initial temperature distributions
• A semigroup version of the isoperimetric inequality
• On a characterization of perimeters in \(\mathbb R^N\) via heat semigroup
• Short-time heat flow and functions of bounded variation in \(\mathbb R^N\)
• Heat content and Hardy inequality for complete Riemannian manifolds
• Off diagonal short time asymptotics for fundamental solution of diffusion equation

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