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.
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Hua, B. Generalized Liouville theorem in nonnegatively curved Alexandrov spaces. Chin. Ann. Math. Ser. B 30, 111–128 (2009). https://doi.org/10.1007/s11401-008-0376-3
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DOI: https://doi.org/10.1007/s11401-008-0376-3