Heat semigroup on a complete Riemannian manifold
Let M be a complete Riemannian manifold and p(t,x,y) the minimal heat kernel on M. Let \(P_ t\) be the associated semigroup. The stochastic completeness \((\int_{M}p(t,x,y)dy=1\), \(t>0)\) and a \(C_ 0\)-diffusion property \((P_ tf\) vanishes at infinity for all \(t>0\) whenever f does) are investigated.
scientific article; zbMATH DE number 4137073