Remarks on the abelian convexity theorem
Differential Geometry
2018-10-09 v2
Abstract
This note contains some observations on abelian convexity theorems. Convexity along an orbit is established in a very general setting using Kempf-Ness functions. This is applied to give short proofs of the Atiyah-Guillemin-Sternberg theorem and of abelian convexity for the gradient map in the case of a real analytic submanifold of complex projective space. Finally we give an application to the action on the probability measures.
Cite
@article{arxiv.1801.01778,
title = {Remarks on the abelian convexity theorem},
author = {Leonardo Biliotti and Alessandro Ghigi},
journal= {arXiv preprint arXiv:1801.01778},
year = {2018}
}
Comments
To appear on Proceedings of the American Mathematical Society