Short-time behavior of the heat kernel and Weyl's law on $RCD^*(K, N)$-spaces

David Tewodrose; Luigi Ambrosio; Shouhei Honda

arxiv: 1701.03906 · v1 · pith:AOP2JH54new · submitted 2017-01-14 · 🧮 math.MG · math.AP· math.DG· math.FA

Short-time behavior of the heat kernel and Weyl's law on RCD^*(K, N)-spaces

Luigi Ambrosio , Shouhei Honda , David Tewodrose This is my paper

classification 🧮 math.MG math.APmath.DGmath.FA

keywords heatspacesbehaviorkernelresultsshort-timeweylconvergence

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In this paper, we prove pointwise convergence of heat kernels for mGH-convergent sequences of $RCD^*(K,N)$-spaces. We obtain as a corollary results on the short-time behavior of the heat kernel in $RCD^*(K,N)$-spaces. We use then these results to initiate the study of Weyl's law in the $RCD$ setting

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Short-time behavior of the heat kernel and Weyl's law on RCD^*(K, N)-spaces

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