The $L^{\infty }$-positivity preserving property and stochastic completeness

Andrea Bisterzo, Ludovico Marini

We say that a Riemannian manifold satisfies the $L^p$-positivity preserving property if $(-\Delta +1)u\ge 0$ in a distributional sense implies $u\ge 0$ for all $u\in L^p$.While geode…