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

Alberto G. Setti; G. Pacelli Bessa; Stefano Pigola

arxiv: 1111.4074 · v1 · pith:HVQN7W2Unew · submitted 2011-11-17 · 🧮 math.DG

On the L¹-Liouville property of stochastically incomplete manifolds

G. Pacelli Bessa , Stefano Pigola , Alberto G. Setti This is my paper

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keywords stochasticallyaddressalexanderclassicalcompleteconstantextentfunctions

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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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On the L¹-Liouville property of stochastically incomplete manifolds

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