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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

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

Related publications

inJournal
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