• A remark on the Alexandrov–Fenchel inequality 

      Wang, Xu (Journal article; Peer reviewed, 2018)
      In this article, we give a complex-geometric proof of the Alexandrov–Fenchel inequality without using toric compactifications. The idea is to use the Legendre transform and develop the Brascamp–Lieb proof of the Prékopa ...
    • Some results on the Hard Lefschetz Condition 

      Tomassini, Adriano; Wang, Xu (Journal article; Peer reviewed, 2018)
      We discuss the Hard Lefschetz Condition (HLC) on various cohomology groups and verify them for the Nakamura manifold of completely solvable type and the Kodaira-Thurston manifold. A general Demailly-Griffiths-Kähler identity ...
    • Vertical-horizontal decomposition of Laplacians and cohomologies of manifolds with trivial tangent bundles 

      Rollenske, Sonke; Tomassini, Adriano; Wang, Xu (Journal article; Peer reviewed, 2019)
      In this paper, we obtain a vertical–horizontal decomposition formula of Laplacians on manifolds with a special foliation structure. Two Nomizu-type theorems for cohomologies of nilmanifolds follow as applications.