Proposition 5.14.21`3EDBDD31B3F1`

Proposition 5.14.21.3EDBDD31B3F1 Let $\Omega \subseteq \mathbb {C}^ n$ be a domain, let $D \Subset \Omega $ be a strongly pseudoconvex domain, and let $\varphi \in \mathrm{PSH}(\Omega )$ be locally bounded. Then there exists a unique locally bounded $\psi \in \mathrm{PSH}(\Omega )$ such that

\[ \begin{cases} \left(\mathrm{dd}^{\mathrm{c}}\psi \right)^ n = 0& \textup{on } D,\\ \psi = \varphi & \textup{on } \Omega \setminus D. \end{cases} \]

Moreover, $\psi \geq \varphi $.

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BibTeX citation

@misc{pome-tag-3EDBDD31B3F1,
  author = {{Pome contributors}},
  title = {Proposition 5.14.21},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/3EDBDD31B3F1/}
}

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Proposition 5.14.213EDBDD31B3F1

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Proposition 5.14.21`3EDBDD31B3F1`