Toric pluripotential theory

Dan Coman, Vincent Guedj, Sibel Sahin, Ahmed Zeriahi Annales Polonici Mathematici MSC: Primary 32W20; Secondary 32U05, 32U20, 32U25, 14M25. DOI: 10.4064/ap180409-3-7 Opublikowany online: 12 October 2018

Streszczenie

We study finite energy classes of quasiplurisubharmonic functions in the setting of toric compact Kähler manifolds. We characterize toric quasiplurisubharmonic functions and give necessary and sufficient conditions for them to have finite (weighted) energy, both in terms of the associated convex function in $\mathbb {R}^n$, and through the integrability properties of its Legendre transform. We characterize log-Lipschitz convex functions on the Delzant polytope, showing that they correspond to toric quasiplurisubharmonic functions which satisfy a certain exponential integrability condition. In the particular case of dimension one, those log-Lipschitz convex functions of the polytope correspond to Hölder continuous toric quasisubharmonic functions.

Autorzy

  • Dan ComanDepartment of Mathematics
    Syracuse University
    Syracuse, NY 13244-1150, U.S.A.
    e-mail
  • Vincent GuedjInstitut de Mathématiques de Toulouse
    Université de Toulouse
    CNRS, UPS
    118 route de Narbonne
    31062 Toulouse Cedex 09, France
    e-mail
  • Sibel SahinDepartment of Mathematics
    Mimar Sinan Fine Arts University
    Istanbul, Turkey
    e-mail
  • Ahmed ZeriahiInstitut de Mathématiques de Toulouse
    Université de Toulouse
    CNRS, UPS
    118 route de Narbonne
    31062 Toulouse Cedex 09, France
    e-mail

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