A note on local gradient estimate on Alexandrov spaces

Bobo Hua and Chao Xia

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Submission date: 18. Feb. 2014
Pages: 12
published in: Tohoku mathematical journal, 66 (2014) 2, p. 259-267 
DOI number (of the published article): 10.2748/tmj/1404911862
Bibtex
MSC-Numbers: 51F99, 51K10, 53C21, 31C05
Keywords and phrases: Alexandrov space, harmonic function, Yau’s gradient estimate
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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.