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arXiv · 2605.29258

Weak solutions of the generalized Monge-Amp\`ere equation and the supercritical deformed Hermitian-Yang-Mills equation: boundary cases

Rei Murakami
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Abstract

We prove the existence and uniqueness of weak solutions for the generalized Monge-Amp\`ere equation and the supercritical deformed Hermitian-Yang-Mills equation in cohomology classes lying on the boundary of the solvable region. Moreover, we prove that the associated geometric flows converge to the weak solutions in the sense of currents. The proof combines viscosity-theoretic and pluripotential-theoretic techniques.

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Rei Murakami. 2026-05-28. Weak solutions of the generalized Monge-Amp\`ere equation and the supercritical deformed Hermitian-Yang-Mills equation: boundary cases. https://arxiv.org/abs/2605.29258

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