TITLE: Convexity radius of a Lie Group
QUESTION [5 upvotes]: Is there a nice formula/method to find the convexity radius of a matrix Lie group (the manifold can be noncompact) ?
Edited based on comments:
Definition : Convexity Radius (Berger - Panoramic View of Riemannian Geometry)
The convexity radius of a Riemannian manifold $M$ is the
infimum of positive numbers $r$ such that the metric open ball $B(m,r)$ is
convex for every $m ∈ M$.

REPLY [4 votes]: For simply connected Lie group with bi-invariant metric it is half of the distance to the cut locus.