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