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• W3043115917 abstract "Abstract In this article, we prove a general and rather flexible upper bound for the heat kernel of a weighted heat operator on a closed manifold evolving by an intrinsic geometric flow. The proof is based on logarithmic Sobolev inequalities and ultracontractivity estimates for the weighted operator along the flow, a method that was previously used by Davies ( Amer. J. Math . 109 (1987) 319–334) in the case of a non‐evolving manifold. This result directly implies Gaussian‐type upper bounds for the heat kernel under certain bounds on the evolving distance function; in particular we find new proofs of Gaussian heat kernel bounds on manifolds evolving by Ricci flow with bounded curvature or positive Ricci curvature. We also obtain similar heat kernel bounds for a class of other geometric flows." @default.
• W3043115917 created "2020-07-23" @default.
• W3043115917 creator A5081201220 @default.
• W3043115917 creator A5085635950 @default.
• W3043115917 date "2023-07-27" @default.
• W3043115917 modified "2023-10-14" @default.
• W3043115917 title "Gaussian upper bounds for the heat kernel on evolving manifolds" @default.
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• W3043115917 doi "https://doi.org/10.1112/jlms.12793" @default.
• W3043115917 hasPublicationYear "2023" @default.
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