@article{Lin2012LogconcavityAS,
title={Log-concavity and symplectic flows},
author={Yi Lin and '. Pelayo},
journal={arXiv: Symplectic Geometry},
year={2012}
}

Let M be a compact, connected symplectic 2n-dimensional manifold on which an(n-2)-dimensional torus T acts effectively and Hamiltonianly. Under the assumption that there is an effective complementary 2-torus acting on M with symplectic orbits, we show that the Duistermaat-Heckman measure of the T-action is log-concave. This verifies the logarithmic concavity conjecture for a class of inequivalent T-actions. Then we use this conjecture to prove the following: if there is an effective symplectic… CONTINUE READING