Preservation of F-convexity under the heat flow

Kazuhiro Ishige; Troy Petitt; Paolo Salani

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arXiv · 2603.10920

Preservation of F-convexity under the heat flow

Kazuhiro Ishige·Troy Petitt·Paolo Salani

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Abstract

We introduce the notion of F-convexity as a general extension of power convexity. We characterize the F-convexities preserved under the heat flow in the n-dimensional Euclidean space, and identify the strongest and the weakest ones among them. We also characterize the F-convexities preserved under the Dirichlet heat flow in convex domains.

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Kazuhiro Ishige, Troy Petitt, Paolo Salani. 2026-03-11. Preservation of F-convexity under the heat flow. https://arxiv.org/abs/2603.10920

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