Revista Matemática Iberoamericana
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Published online: 2019-06-27
On biparabolicity of Riemannian manifoldsShokoufe Faraji and Alexander Grigor'yan (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