Laplacian comparison for Alexandrov spaces
Differential Geometry
2007-09-07 v1 Metric Geometry
Abstract
We consider an infinitesimal version of the Bishop-Gromov relative volume comparison condition as generalized notion of Ricci curvature bounded below for Alexandrov spaces. We prove a Laplacian comparison theorem for Alexandrov spaces under the condition. As an application we prove a topological splitting theorem.
Cite
@article{arxiv.0709.0788,
title = {Laplacian comparison for Alexandrov spaces},
author = {Kazuhiro Kuwae and Takashi Shioya},
journal= {arXiv preprint arXiv:0709.0788},
year = {2007}
}
Comments
30 pages, 1 figure