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arXiv · 1712.06911

The Dirichlet problem for the complex Hessian operator in the class $\mathcal{N}_m(H)$

Ayoub El-Gasmi
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Abstract

We prove that, in a $m$-hyperconvex domain in $\mathbb{C}^{n},$ if a non-negative Borel measure is dominated by a complex Hessian measure, then it is a complex Hessian measure of a function in the class $\mathcal{N}_m(H)$. This is an extension of P. {\AA}hg, U. Cegrell, R. Czy\.z and P.H. Hiep's result in \cite{ACCH}.

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Ayoub El-Gasmi. 2017-12-19. The Dirichlet problem for the complex Hessian operator in the class $\mathcal{N}_m(H)$. https://arxiv.org/abs/1712.06911

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