Generalized Liouville theorem in nonnegatively curved Alexandrov spaces

Abstract

In this paper, Yau’s conjecture on harmonic functions in Riemannian manifolds is generalized to Alexandrov spaces. It is proved that the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional and strong Liouville theorem holds in Alexandrov spaces with nonnegative curvature.

Keywords

Alexandrov space / Harmonic function / Harnack inequality

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