Log-concavity of complexity one Hamiltonian torus actions

Abstract

Let $(M,\omega )$ be a closed $2n$-dimensional symplectic manifold equipped with a Hamiltonian $T^{n-1}$-action. Then Atiyah-Guillemin-Sternberg convexity theorem implies that the image of the moment map is an $(n-1)$-dimensional convex polytope. In this paper, we show that the density function of the Duistermaat-Heckman measure is log-concave on the image of the moment map.

5 pages, 1 figure

References in corpus (1)

• The log-concavity conjecture on semifree symplectic S^1-manifolds with isolated fixed points