Shadow geometry at singular points of CAT(k) spaces
Metric Geometry
2023-11-17 v1
Abstract
In any CAT(k) space M, the "shadow" of a tangent vector Z at a point p is the set vectors that form an angle of \pi or more with Z. Taking logarithm maps at points approaching p along a fixed geodesic ray from p with tangent Z collapses the shadow to a single ray while leaving isometrically intact every convex cone that avoids the shadow of Z.
Keywords
Cite
@article{arxiv.2311.09451,
title = {Shadow geometry at singular points of CAT(k) spaces},
author = {Jonathan C. Mattingly and Ezra Miller and Do Tran},
journal= {arXiv preprint arXiv:2311.09451},
year = {2023}
}
Comments
19 pages, 8 figures. This is the first in a four-part series leading to central limit theorems on stratified spaces