Tohoku Mathematical Journal
2014

June
SECOND SERIES VOL. 66, NO. 2

Tohoku Math. J.
66 (2014), 259-267

Title A NOTE ON LOCAL GRADIENT ESTIMATE ON ALEXANDROV SPACES

Author Bobo Hua and Chao Xia

(Received January 22, 2013, revised June 10, 2013)
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 in [24]. Our result improves the previous one of Zhang-Zhu [24] in the case of negative Ricci lower bound.

Mathematics Subject Classification. Primary 51F99; Secondary 51K10, 53C21,31C05.

Key words and phrases. Alexandrov spaces, harmonic functions, Yau's gradient estimate.

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