A note on local gradient estimate on Alexandrov spaces
arXiv:1301.4810
Abstract
In this note, we prove Cheng-Yau type local gradient estimate for harmonic functions on Alexandrov spaces with Ricci curvature bounded below. We adopt a refined version of Moser's iteration which is based on Zhang-Zhu's Bochner type formula. Our result improves the previous one of Zhang-Zhu in the case of negative Ricci lower bound.
10 pages, a revision, to appear in Tohoku Math. J. (2)