Heat kernel estimates on connected sums with non-compact joint

Satoshi Ishiwata (Univ. of Tsukuba)

Abstract: In 2009, Grigor'yan and Saloff-Coste proved sharp
heat kernel estimates on manifolds with ends.
As a generalization of their result, we consider
heat kernel estimates on connected sums whose joint is
not necessarily compact. As a main result, we obtain
sharp heat kernel estimate on a connected sum of two
copies of a Euclidean space along a revolution.
This is a joint work with Alexander Grigor'yan.