Laplacian comparison for Alexandrov spaces
arXiv:0709.0788
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.
30 pages, 1 figure