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Heat kernel bounds and Ricci curvature for Lipschitz manifolds

Author

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  • Braun, Mathias
  • Rigoni, Chiara

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.

Suggested Citation

  • Braun, Mathias & Rigoni, Chiara, 2024. "Heat kernel bounds and Ricci curvature for Lipschitz manifolds," Stochastic Processes and their Applications, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:spapps:v:170:y:2024:i:c:s0304414923002648
    DOI: 10.1016/j.spa.2023.104292
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