Laplacian comparison for Alexandrov spaces

Details Laplacian comparison for Alexandrov spaces Laplacian comparison for Alexandrov spaces

2007-09-06

arxiv.org/abs/0709.0788v1

Mathematics

Differential Geometry

30 pages, 1 figure

Scientific paper

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.

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