The log-concavity conjecture on semifree symplectic S¹-manifolds with isolated fixed points

الأصل · EN

Let (M,ω) be a closed 2n-dimensional semifree Hamiltonian S¹-manifold with only isolated fixed points. We prove that a density function of the Duistermaat-Heckman measure is log-concave. Moreover, we prove that (M,ω) and any reduced symplectic form satisfy the Hard Lefschetz property.