  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.
