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arXiv · 2405.03982

Non-preservation of concavity properties by the Dirichlet heat flow on Riemannian manifolds

Kazuhiro Ishige·Asuka Takatsu·Haruto Tokunaga
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Abstract

We prove that no concavity properties are preserved by the Dirichlet heat flow in a totally convex domain of a Riemannian manifold unless the sectional curvature vanishes everywhere on the domain.

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Kazuhiro Ishige, Asuka Takatsu, Haruto Tokunaga. 2024-05-07. Non-preservation of concavity properties by the Dirichlet heat flow on Riemannian manifolds. https://arxiv.org/abs/2405.03982

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