Yau's gradient estimates on Alexandrov spaces
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.
math.DG↗
arXiv subjects
Hui-Chun Zhang
Publications and source records attributed to Hui-Chun Zhang.
Ricci Curvature on Alexandrov spaces and Rigidity Theorems
In this paper, we introduce a new notion for lower bounds of Ricci curvature on Alexandrov spaces, and extend Cheeger-Gromoll splitting theorem and Cheng's maximal diameter theorem to Alexandrov spaces under this Ricci curvature condition.
math.DG↗
On a new definition of Ricci curvature on Alexandrov spaces
Recently, in [49], a new definition for lower Ricci curvature bounds on Alexandrov spaces was introduced by the authors. In this article, we extend our research to summarize the geometric and analytic results under this Ricci condition. In particular, two new results, the rigidity result of Bishop-Gromov volume comparison and Lipschitz continuity of heat kernel, are obtained.
math.DG↗