Harmonic functions on metric measure spaces
Analysis of PDEs
2016-03-17 v2 Metric Geometry
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.
Cite
@article{arxiv.1308.3607,
title = {Harmonic functions on metric measure spaces},
author = {Bobo Hua and Martin Kell and Chao Xia},
journal= {arXiv preprint arXiv:1308.3607},
year = {2016}
}
Comments
21 pages, comments are welcome!