@article{c7705c4181e740589a27f34cb91b6800,
title = "Toric pluripotential theory",
abstract = "We study finite energy classes of quasiplurisubharmonic functions in the setting of toric compact K{\"a}hler 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 H{\"o}lder continuous toric quasisubharmonic functions.",
keywords = "Amp{\`e}re operator, Complex Monge, Delzant polytope, Lelong number, Quasiplurisubharmonic function, Toric manifold",
author = "Dan Coman and Vincent Guedj and Sibel Sahin and Ahmed Zeriahi",
note = "Funding Information: Dan Coman is partially supported by the NSF Grant DMS-1700011. Vincent Guedj and Ahmed Zeriahi are partially supported by the ANR project GRACK. Sibel Sahin is supported by the T{\"U}BİTAK 2219 postdoctoral grant. Funding Information: This paper is dedicated to the memory of Professor J?zef Siciak, who started a systematical study of extremal plurisubharmonic functions in the early sixties, laying the first stones of Pluripotential Theory. His ideas have been very influential. The paper was written during the postdoctoral research period of the third named author at l?Institut de Math?matiques de Toulouse. She is grateful to her co-authors for their endless support and hospitality during the stay. Dan Coman is partially supported by the NSF Grant DMS-1700011. Vincent Guedj and Ahmed Zeriahi are partially supported by the ANR project GRACK. Sibel Sahin is supported by the T?B?TAK 2219 postdoctoral grant. Publisher Copyright: {\textcopyright} Instytut Matematyczny PAN, 2019.",
year = "2019",
doi = "10.4064/ap180409-3-7",
language = "English (US)",
volume = "123",
pages = "215--242",
journal = "Annales Polonici Mathematici",
issn = "0066-2216",
publisher = "Polska Akademia Nauk,Instytut Matematycznys",
number = "1",
}