Weak limits of the J-flow and the deformed Hermitian-Yang-Mills flow on Kähler surfaces: boundary cases

2024/03/30 by Rei Murakami, Murakami, Rei
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2404.00501

Abstract

We prove that if a pair of Kähler classes is J-nef, the J-flow on a compact Kähler surface converges to a weak solution of the Monge-Ampère equation in the sense of currents. We also establish the same convergence behavior for the deformed Hermitian-Yang-Mills flow. The method is based on a property of a limit of viscosity subsolutions.

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