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arXiv · 1804.03387

Toric Pluripotential Theory

Vincent Guedj·Ahmed Zeriahi·Dan Coman·Sibel Sahin
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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.

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BibTeXRIS

Vincent Guedj, Ahmed Zeriahi, Dan Coman, Sibel Sahin. 2018-04-10. Toric Pluripotential Theory. https://arxiv.org/abs/1804.03387

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