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MiS Preprint
22/2014
A note on local gradient estimate on Alexandrov spaces
Bobo Hua and Chao Xia
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 formulAa. Our result improves the previous one of Zhang-Zhu in the case of negative Ricci lower bound.
