On the $L^1$-Liouville property of stochastically incomplete manifolds

Abstract

A classical result by Alexander Grigor'yan states that on a stochastically complete manifold the non-negative superharmonic $L^1$-functions are necessarily constant. In this paper we address the question of whether and to what extent the reverse implication holds.

References in corpus (1)

• Stochastic completeness and volume growth