English

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 κ>0\kappa>0) of a CAT(κ)CAT(\kappa) space is convex.

Keywords

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