Toric Pluripotential Theory
Complex Variables
2018-04-11 v1 Differential Geometry
Abstract
We study finite energy classes of quasiplurisubharmonic (qpsh) functions in the setting of toric compact K{\"a}hler 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 H{\"o}lder continuous toric quasisubharmonic functions.
Cite
@article{arxiv.1804.03387,
title = {Toric Pluripotential Theory},
author = {Vincent Guedj and Ahmed Zeriahi and Dan Coman and Sibel Sahin},
journal= {arXiv preprint arXiv:1804.03387},
year = {2018}
}