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arXiv · 1308.3607

Harmonic functions on metric measure spaces

Bobo Hua·Martin Kell·Chao Xia
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Abstract

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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Bobo Hua, Martin Kell, Chao Xia. 2013-08-16. Harmonic functions on metric measure spaces. https://arxiv.org/abs/1308.3607

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