Alessandro Goffi — Neckpinchhttps://neckpinch.com/authors/alessandro-goffi/New arXiv papers by Alessandro Goffi, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT Regularizing estimates for positive solutions of the heat equation under geometric flowshttps://neckpinch.com/papers/2608.16743/arxiv:2608.16743Mon, 17 Aug 2026 00:00:00 GMTAlessandro Goffi, Francesco Pediconi — 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.Ricci flow