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arXiv · 2609.18594

Heat kernel on Ricci shrinker metric measure spaces

Bing Wang·Jie Wang
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Abstract

As a metric measure space possessing positive Bakry-Émery curvature, a Ricci shrinker with potential function $f$ admits a heat kernel $H_f$ under the weighted volume measure $e^{-f}dv$. In this paper, we study $H_f$ systematically and establish a series of fundamental estimates. Moreover, we clarify the equivalence between $H_f$ and the spacetime heat kernel $H(x,t;y,s)$ under Ricci flow induced by a Ricci shrinker. Inspired by this relation, we extend corresponding analysis tools of Ricci flows to Ricci shrinker metric measure spaces, such as Nash entropy and reduced distance. As a direct application, we prove that $\left|\nabla R\right|=o(f^{3/2})$ implies $R=o(f)$.

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Bing Wang, Jie Wang. 2026-09-16. Heat kernel on Ricci shrinker metric measure spaces. https://arxiv.org/abs/2609.18594

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