The Extension of Holomorphic Functions on a Non-Pluriharmonic Locus | Graduate School of Mathematical Sciences, The University of Tokyo

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The Extension of Holomorphic Functions on a Non-Pluriharmonic Locus

J. Math. Sci. Univ. Tokyo
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.

Mathematical Reviews Number: MR4586456

Received: 2022-09-29

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