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Complex Manifolds

Ed. by Fino, Anna Maria

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Convexity theorems for the gradient map on probability measures

Leonardo Biliotti
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  • Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy
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/ Alberto Raffero
  • Dipartimento di Matematica e Informatica “U. Dini”, Università degli Studi di Firenze, Viale Morgagni 67/a, 50134 Firenze, Italy
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Published Online: 2018-07-05 | DOI: https://doi.org/10.1515/coma-2018-0008


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.

Keywords : Gradient map; Probability measures; Convexity

MSC 2010: 53D20


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About the article

Received: 2018-02-16

Accepted: 2018-06-03

Published Online: 2018-07-05

Citation Information: Complex Manifolds, Volume 5, Issue 1, Pages 133–145, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2018-0008.

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© 2018 Leonardo Biliotti and Alberto Raffero, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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