Heat flow in Riemannian manifolds with non-negative Ricci curvature

Michiel van den Berg

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arXiv · 1506.07063

Heat flow in Riemannian manifolds with non-negative Ricci curvature

Michiel van den Berg

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Abstract

Let $Ω$ be an open set in a geodesically complete, non-compact, $m$-dimen-sional Riemannian manifold $M$ with non-negative Ricci curvature, and without boundary. We study the heat flow from $Ω$ into $M-Ω$ if the initial temperature distribution is the characteristic function of $Ω$. We obtain a necessary and sufficient condition which ensures that an open set $Ω$ with infinite measure has finite heat content for all $t>0$. We also obtain upper and lower bounds for the heat content of $Ω$ in $M$. Two-sided bounds are obtained for the heat loss of $Ω$ in $M$ if the measure of $Ω$ is finite.

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BibTeX RIS

Michiel van den Berg. 2018-01-31. Heat flow in Riemannian manifolds with non-negative Ricci curvature. https://arxiv.org/abs/1506.07063

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