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arXiv · 2203.07232

The Dirichlet problem for Monge-Amp\`ere equation for $(n-1)$-PSH functions on Hermitian manifolds

Rirong Yuan
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Abstract

We solve the Dirichlet problem for Monge-Amp\`ere equation for $(n-1)$-PSH functions possibly with degenerate right-hand side, through deriving a quantitative version of boundary estimate under the assumption of $(n-1)$-PSH subsolutions. In addition, we confirm the subsolution assumption on a product of a closed balanced manifold with a compact Riemann surface with boundary.

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Rirong Yuan. 2022-03-14. The Dirichlet problem for Monge-Amp\`ere equation for $(n-1)$-PSH functions on Hermitian manifolds. https://arxiv.org/abs/2203.07232

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