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Measures of finite energy in pluripotential theory: a synthetic approach

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arxiv 2307.01697 v1 pith:JAJLDJRP submitted 2023-07-04 math.CV math.DG

Sebastien Boucksom , Mattias Jonsson This is my paper · ORCID
classification math.CVmath.DG
keywords energyapproachfinitefunctionalsintroducemeasurespluripotentialspace
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We introduce a synthetic approach to global pluripotential theory, covering in particular the case of a compact K\"ahler manifold and that of a projective Berkovich space over a non-Archimedean field. We define and study the space of measures of finite energy, introduce twisted energy and free energy functionals thereon, and show that coercivity of these functionals is an open condition with respect to the polarization.

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  1. A transcendental non-Archimedean Calabi--Yau Theorem with applications to the cscK problem

    math.AG 2025-09 conditional novelty 8.0 of 10

    Uniform K-stability for models implies existence and uniqueness of a cscK metric in any Kähler class, including transcendental (non-projective) classes.

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