A note on local gradient estimate on Alexandrov spaces

Published 21 Jan 2013 in math.MG | (1301.4810v2)

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.

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