Revista Matemática Iberoamericana


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Volume 35, Issue 7, 2019, pp. 2025–2034
DOI: 10.4171/rmi/1108

Published online: 2019-06-27

On biparabolicity of Riemannian manifolds

Shokoufe Faraji[1] and Alexander Grigor'yan[2]

(1) Universität Bielefeld, Germany
(2) Universität Bielefeld, Germany and Russian Academy of Sciences, Moscow, Russia

A Riemannian manifold is called biparabolic if any positive bisuperharmonic function is harmonic. We provide a criterion of biparabolicity in terms of the Green function of the Laplacian, as well as a sharp sufficient condition for biparabolicity in terms of the volume growth function.

Keywords: Biparabolic manifolds, parabolic manifolds, Green function, heat kernel

Faraji Shokoufe, Grigor'yan Alexander: On biparabolicity of Riemannian manifolds. Rev. Mat. Iberoam. 35 (2019), 2025-2034. doi: 10.4171/rmi/1108