Uniqueness of L¹ harmonic functions on rotationally symmetric Riemannian manifolds

抄録

We show that any rotationally symmetric Riemannian manifold has the L¹-Liouville property for harmonic functions, i.e., any integrable harmonic function on it must be identically constant. We also give a characterization of a manifold which carries a non-constant L¹ nonnegative subharmonic function.