Holomorphic Disc Foliations and the local Regularity of the HCMA Equation

Abstract: The HCMA equation plays a central role in Kähler geometry, where it describes geodesics in the space of Kähler metrics. A major open problem concerns the regularity of weak solutions to this equation. This problem is closely connected to questions of existence and uniqueness of constant scalar curvature Kähler metrics.

In this talk, I will present a new local higher regularity result for the HCMA equation on Kähler manifolds. The approach is based on holomorphic disc foliations and pluripotential theory, together with a Nash–Moser argument to handle a subtle loss of regularity in the construction. As an application, I will discuss the consequences of this regularity on the ALE end.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

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CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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