On the L¹-Liouville property of stochastically incomplete manifolds

2011/11/17 by G. Pacelli Bessa, Bessa, G. Pacelli, Stefano Pigola +3
Mathematics · #31C12 #58J65 #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1111.4074

openalex publication_date 2011/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A classical result by Alexander Grigor'yan states that on a stochastically complete manifold the non-negative superharmonic L¹-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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