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Geometric pluripotential theory on K\"ahler manifolds

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arxiv 1902.01982 v2 pith:LUYZUSRY submitted 2019-02-06 math.DG math.CV

Tamás Darvas This is my paper · ORCID
classification math.DGmath.CV
keywords theoryahlercomplexequationsgeometrymonge-amppluripotentialproblems
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Finite energy pluripotential theory accommodates the variational theory of equations of complex Monge-Amp\`ere type arising in K\"ahler geometry. Recently it has been discovered that many of the potential spaces involved have a rich metric geometry, effectively turning the variational problems in question into problems of infinite dimensional convex optimization, yielding existence results for solutions of the underlying complex Monge-Amp\`ere equations. The purpose of this survey is to describe these developments from basic principles.

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  1. Existence of Kahler-Ricci solitons on smoothable Q-Fano varities

    math.DG 2019-08 conditional novelty 6.0 of 10

    K-stable smoothable Q-Fano varieties admit Kähler-Ricci solitons, extending the Yau-Tian-Donaldson correspondence for solitons from the smooth case to the singular smoothable case.

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