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On the Dirichlet Parabolicity and the L¹-Liouville Property

Leandro Pessoa
Universidade Federal do Piauí
Luigi Stasi Seminar Room, ICTP
Thursday, February 15, 2018 - 14:00

In this talk we will discuss on the L¹-Liouville property for positive, superharmonic functions by providing many evidences that its validity relies on geometric conditions localized on large enough portions of the space. By the way, we present some examples in any dimension showing that the L¹-Liouville property is strictly weaker than the stochastic completeness of the manifold. The main tool in our investigations is represented by the potential theory of a manifold with boundary subject to Dirichlet boundary conditions. This is a joint work with Professors Stefano Pigola and Alberto G. Setti (Università degli Studi dell'Insubria – Italia)

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