Heat kernel bounds and Ricci curvature for Lipschitz manifolds

Mathias Braun and Chiara Rigoni

Stochastic Processes and their Applications, 2024, vol. 170, issue C

Abstract: Given any d-dimensional Lipschitz Riemannian manifold (M,g) with heat kernel p, we establish uniform upper bounds on p which can always be decoupled in space and time. More precisely, we prove the existence of a constant C>0 and a bounded Lipschitz function R:M→(0,∞) such that for every x∈M and every t>0, supy∈Mp(t,x,y)≤Cmin{t,R2(x)}−d/2.This allows us to identify suitable weighted Lebesgue spaces w.r.t. the given volume measure as subsets of the Kato class induced by (M,g). In the case ∂M≠0̸, we also provide an analogous inclusion for Lebesgue spaces w.r.t. the surface measure on ∂M.

Keywords: Lipschitz manifold; Heat kernel; Kato class; Ricci curvature (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.104292

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