Log-concavity of complexity one Hamiltonian torus actions

Details Log-concavity of complexity one Hamiltonian torus actions Log-concavity of complexity one Hamiltonian torus actions

2011-09-14

arxiv.org/abs/1109.3115v1

Mathematics

Symplectic Geometry

5 pages, 1 figure

Scientific paper

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.

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