Large time behavior of the on-diagonal heat kernel for minimal submanifolds with polynomial volume growth

Abstract

In this paper we provide a lower bound for the long time on-diagonal heat kernel of minimal submanifolds in a Cartan-hadamard ambient manifold assuming that the submanifold is of polynomial volume growth. In particular cases, that lower bound is related with the number of ends of the submanifold.

arXiv comment8 pages, 3 figures

References in corpus (1)

• Large time behavior of the heat kernel