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arXiv · 2112.10042

The Dirichlet problem for the Monge-Amp\`ere equation on Hermitian manifolds with boundary

Slawomir Kolodziej·Ngoc Cuong Nguyen
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Abstract

We study weak quasi-plurisubharmonic solutions to the Dirichlet problem for the complex Monge-Am\`ere equation on a general Hermitian manifold with non-empty boundary. We prove optimal subsolution theorems: for bounded and H\"older continuous quasi-plurisubharmonic functions. The continuity of the solution is proved for measures that well dominated by capacity, for example measures with $L^p$, $p>1$ densities, or moderate measures in the sense of Dinh-Nguyen-Sibony.

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Slawomir Kolodziej, Ngoc Cuong Nguyen. 2021-12-19. The Dirichlet problem for the Monge-Amp\`ere equation on Hermitian manifolds with boundary. https://arxiv.org/abs/2112.10042

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