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March 14, 2026Annals of Global Analysis and Geometry0 citationsOpen Access

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

RMRei Murakami

Key Points

  • This research aims to analyze the convergence of J-flow and deformed Hermitian-Yang-Mills flow on compact Kähler surfaces.
  • Proved convergence to a weak solution of the Monge-Ampère equation.
  • Established convergence behavior for deformed Hermitian-Yang-Mills flow.
  • Used properties of limit of viscosity subsolutions for the analysis.
  • J-flow converges to a weak solution of the Monge-Ampère equation in the sense of currents.
  • Deformed Hermitian-Yang-Mills flow shows similar convergence behavior.
  • Results highlight the importance of J-nef classes in this convergence.

Abstract

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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Cite This Study

Rei Murakami (2026) studied this question.

synapsesocial.com/papers/69b4fc1fb39f7826a300cc29https://doi.org/10.1007/s10455-026-10032-9
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