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

created by ambrosio on 14 Jan 2017

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Inserted: 14 jan 2017
Last Updated: 14 jan 2017

Year: 2017

Abstract:

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.