Yau's gradient estimates on Alexandrov spaces
Hui-Chun Zhang, Xi-Ping Zhu
TL;DR
This paper extends Yau's gradient estimates for harmonic functions to Alexandrov spaces with Ricci curvature bounds, using a Bochner type formula, advancing geometric analysis in non-smooth spaces.
Contribution
It introduces a Bochner type formula and proves Yau's gradient estimate on Alexandrov spaces, a significant generalization from smooth manifolds.
Findings
Established a Bochner type formula on Alexandrov spaces
Proved Yau's gradient estimate for harmonic functions in this setting
Extended geometric analysis tools to non-smooth spaces
Abstract
In this paper, we establish a Bochner type formula on Alexandrov spaces with Ricci curvature bounded below. Yau's gradient estimate for harmonic functions is also obtained on Alexandrov spaces.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research