JournalsrmiVol. 35, No. 7pp. 2025–2034

On biparabolicity of Riemannian manifolds

  • Shokoufe Faraji

    Universität Bielefeld, Germany

  • Alexander Grigor'yan

    Universität Bielefeld, Germany and Russian Academy of Sciences, Moscow, Russia
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Abstract

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.

Cite this article

Shokoufe Faraji, Alexander Grigor'yan, On biparabolicity of Riemannian manifolds. Rev. Mat. Iberoam. 35 (2019), no. 7, pp. 2025–2034

DOI 10.4171/RMI/1108