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arXiv · 1604.08029

The Dirichlet problem for a complex Hessian equation on compact Hermitian manifolds with boundary

Dongwei Gu·Ngoc Cuong Nguyen
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Abstract

We solve the classical Dirichlet problem for a general complex Hessian equation on a small ball in $\bC^n$. Then, we show that there is a continuous solution, in pluripotential theory sense, to the Dirichlet problem on compact Hermitian manifolds with boundary that equipped locally conformal Kähler metrics, provided a subsolution.

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Dongwei Gu, Ngoc Cuong Nguyen. 2017-08-22. The Dirichlet problem for a complex Hessian equation on compact Hermitian manifolds with boundary. https://arxiv.org/abs/1604.08029

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