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MiS Preprint

A note on local gradient estimate on Alexandrov spaces

Bobo Hua and Chao Xia


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.

Feb 18, 2014
Feb 25, 2014
MSC Codes:
51F99, 51K10, 53C21, 31C05
Alexandrov space, harmonic function, Yau’s gradient estimate

Related publications

2014 Repository Open Access
Bobo Hua and Chao Xia

A note on local gradient estimate on Alexandrov spaces

In: Tohoku mathematical journal, 66 (2014) 2, pp. 259-267