2018/04/10 by Vincent Guedj, Ahmed Zériahi, Guedj, Vincent +5 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1804.03387
openalex publication_date 2018/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study finite energy classes of quasiplurisubharmonic (qpsh) functions in the setting of toric compact Kähler manifolds. We characterize toric qpsh functions and give necessary and sufficient conditions for them to have finite (weighted) energy, both in terms of the associated convex function in 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 qpsh 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.