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arXiv · 2608.16743

Regularizing estimates for positive solutions of the heat equation under geometric flows

Alessandro Goffi·Francesco Pediconi
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Abstract

We study higher-order global estimates for the heat equation on Riemannian manifolds, both for static metrics and for metrics evolving under the Ricci flow. Under minimal geometric assumptions, we derive first-order regularizing estimates for log-solutions of the heat equation, together with upper second-order bounds with explicit constants. Our quantitative approach is based on integral duality methods proposed by L.\ C.\ Evans, J.-M.\ Lasry and P.-L.\ Lions in different settings.

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Alessandro Goffi, Francesco Pediconi. 2026-08-17. Regularizing estimates for positive solutions of the heat equation under geometric flows. https://arxiv.org/abs/2608.16743

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