Toric pluripotential theory

Dan Coman, Vincent Guedj, Sibel Sahin, Ahmed Zeriahi

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 Rn, 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.

Original languageEnglish (US)
Pages (from-to)215-242
Number of pages28
JournalAnnales Polonici Mathematici
Issue number1
StatePublished - 2019


  • Ampère operator
  • Complex Monge
  • Delzant polytope
  • Lelong number
  • Quasiplurisubharmonic function
  • Toric manifold

ASJC Scopus subject areas

  • General Mathematics


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