Convexity theorems for the gradient map on probability measures

Abstract

Given a Kähler manifold $(Z,J,\omega )$ and a compact real submanifold $M\subset Z$, we study the properties of the gradient map associated with the action of a noncompact real reductive Lie group $\mathrm{G}$ on the space of probability measures on $M.$ In particular, we prove convexity results for such map when $\mathrm{G}$ is Abelian and we investigate how to extend them to the non-Abelian case.

References in corpus (1)

• Stratifications with respect to actions of real reductive groups

Cited by in corpus (1)

• Convexity properties of gradient maps associated to real reductive representations