Volume growth and on-diagonal heat kernel bounds on Riemannian manifolds with an end

Abstract

We investigate heat kernel estimates of the form $p_t(x,x)\ge c_x{t}^{-\alpha },$ for large enough $t,$ where $\alpha$ and $c_x$ are positive reals and $c_x$ may depend on $x,$ on manifolds having at least one end.

30 pages