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

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

2011-11-17

arxiv.org/abs/1111.4074v1

Mathematics

Differential Geometry

Scientific paper

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.

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