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arXiv · 2404.00501

Weak limits of the $J$-flow and the deformed Hermitian-Yang-Mills flow on K\"ahler surfaces: boundary cases

Rei Murakami
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Abstract

We prove that if a pair of K\"ahler classes is $J$-nef, the $J$-flow on a compact K\"ahler surface converges to a weak solution of the Monge-Amp\`ere 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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Rei Murakami. 2024-03-30. Weak limits of the $J$-flow and the deformed Hermitian-Yang-Mills flow on K\"ahler surfaces: boundary cases. https://arxiv.org/abs/2404.00501

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