Convexity theorems for the gradient map on probability measures

Complex Manifolds

Raffero Alberto¹  Biliotti Leonardo² 

[1] Dipartimento di Matematica e Informatica “U. Dini”, Università degli Studi di Firenze, Viale Morgagni 67/a, 50134 Firenze, Italy;Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy;

关键词: Gradient map;    Probability measures;    Convexity;    53D20;   

DOI  :  10.1515/coma-2018-0008

来源: DOAJ

【 摘 要 】

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

【 授权许可】

Unknown