Convexity is a local property in $CAT(\kappa )$ spaces

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

v2: 8 pages, 1 figure. Added some references

References in corpus (2)

• The Center Conjecture for spherical buildings of types F4 and E6
• Local convexity in CAT(κ)-spaces