The Extension of Holomorphic Functions on a Non-Pluriharmonic Locus
Vol. 30 (2023), No. 1, Page 107-123.
Tiba, Yusaku
The Extension of Holomorphic Functions on a Non-Pluriharmonic Locus
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
Abstract:
Let $n \geq 4$ and let $\Omega$ be a bounded hyperconvex domain in $\mathbb{C}^{n}$. Let $\varphi$ be a negative exhaustive smooth plurisubharmonic function on $\Omega$. We show that any holomorphic function defined on a connected open neighborhood of the support of $(i\partial \overline{\partial}\varphi)^{n-3}$ can be extended to a holomorphic function on $\Omega$.
Keywords: plurisubharmonic function, pseudoconvex domain.
Mathematics Subject Classification (2020): 32A10, 32U10.
Received: 2022-09-29
