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arxiv: 1308.3607 · v2 · pith:RLBHKF6Enew · submitted 2013-08-16 · 🧮 math.AP · math.MG

Harmonic functions on metric measure spaces

Bobo Hua , Martin Kell , Chao Xia This is my paper
classification 🧮 math.AP math.MG
keywords spacesfunctionsharmonicmeasuremetriccurvaturericciriemannian
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In this paper, we study harmonic functions on metric measure spaces with Riemannian Ricci curvature bounded from below, which were introduced by Ambrosio-Gigli-Savar\'e. We prove a Cheng-Yau type local gradient estimate for harmonic functions on these spaces. Furthermore, we derive various optimal dimension estimates for spaces of polynomial growth harmonic functions on metric measure spaces with nonnegative Riemannian Ricci curvature.

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  1. Partial regularity of harmonic maps from Alexandrov spaces

    math.DG 2019-07 unverdicted novelty 7.0

    Proves Lipschitz regularity of continuous harmonic maps from finite-dimensional Alexandrov spaces to compact smooth Riemannian manifolds, solving Lin's conjecture by extending Huang-Wang's argument.