Bounded harmonic functions and positive Ricci curvature
Let M be a complete Riemannian manifold. It is known that if M has non- negative Ricci curvature then every bounded harmonic function is constant. This result is extended to the case of a non-negative curvature outside of a compact subset of M and it is then proved that the space of bounded harmonic functions is finite dimensional. Actually it is proved that the map \(f\to df\) from the space of bounded harmonic functions on the space of harmonic one forms has its range in a finite dimensional space and the result follows from the fact that the kernel of this map is one dimensional.
scientific article; zbMATH DE number 3975336
scientific article