Infinitesimal Bishop-Gromov condition for Alexandrov spaces
Kazuhiro Kuwae, Takashi Shioya
TL;DR
This paper establishes an infinitesimal volume comparison condition for Alexandrov spaces, extending geometric analysis tools to these non-smooth spaces.
Contribution
It introduces the infinitesimal Bishop-Gromov condition for Alexandrov spaces, a novel extension of classical volume comparison theorems.
Findings
Proved the infinitesimal Bishop-Gromov condition for Alexandrov spaces
Extended volume comparison techniques to non-smooth metric spaces
Provided new insights into the geometric structure of Alexandrov spaces
Abstract
We prove the infinitesimal version of Bishop-Gromov volume comparison condition for Alexandrov spaces.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometry and complex manifolds