On the Krein-Milman theorem in CAT(κ) spaces.

Let κ>0 and (X, ρ) be a complete CAT(κ) space whose diameter smaller than .... It is shown that if K is a nonempty compact convex subset of X, then K is the closed convex hull of its set of extreme points. This is an extension of the Krein-Milman theorem to the general setting of CAT(κ) spaces. [ABSTRACT FROM AUTHOR]