复杂度为1的Hamilton环面作用的对数周期
Log-concavity of complexity one Hamiltonian torus actions
摘要：
设$(M,ω)$是一个具有Hamilton $T^{n-1}$作用的闭$2n$维辛流形.然后Atiyah-Guillemin-Sternberg凸性定理暗示矩映射的像是$(n-1)$维凸多胞体.本文证明了Duistermaat-Heckman测度的密度函数在矩映射的像上是对数凹的.
英文摘要：
Let $(M,ω)$ 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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