Convexity is a local property in $CAT(\kappa)$ spaces
Metric Geometry
2013-05-08 v2
Abstract
In this note we show that a connected, closed and locally convex subset (with an extra assumption on the diameter with respect to the induced length metric if ) of a space is convex.
Cite
@article{arxiv.1304.4147,
title = {Convexity is a local property in $CAT(\kappa)$ spaces},
author = {Carlos Ramos-Cuevas},
journal= {arXiv preprint arXiv:1304.4147},
year = {2013}
}
Comments
v2: 8 pages, 1 figure. Added some references