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

By Luigi Ambrosio, Shouhei Honda, David Tewodrose. 2017

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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

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d488635963f3e02e471cdb62254cd8e3b6056145