L. Ambrosio - S. Honda - D. Tewodrose

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

preprint

Inserted: 3 may 2023
Last Updated: 3 may 2023

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