Short-time behavior of the heat kernel and Weyl's law on $RC{D}^{\ast }(K,N)$-spaces

Abstract

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

24 pages

Cited by in corpus (1)

• On the asymptotic behavior of the dimension of spaces of harmonic functions with polynomial growth