On biparabolicity of Riemannian manifolds (Q2280519)

A Riemannian manifold is called biparabolic if any positive bi-superharmonic function is harmonic. The authors give a criteria of biparabolicity in terms of the Green function of the Laplacian. They also extend a result of \textit{S. Y. Cheng} and \textit{S.-T. Yau} [Commun. Pure Appl. Math. 28, 333--354 (1975; Zbl 0312.53031)] on the parabolicity of a manifold by giving a sufficient condition for biparabolicity in terms of the volume growth of the geodesic ball of radius \(r\) as \(r\to\infty\).