An extension theorem of holomorphic functions on hyperconvex domains

Seungjae Lee; Yoshikazu Nagata

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arXiv · 1811.06438

An extension theorem of holomorphic functions on hyperconvex domains

Seungjae Lee·Yoshikazu Nagata

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Abstract

Let $n \geq 3$ and $Ω$ be a bounded domain in $\mathbb{C}^n$ with a smooth negative plurisubharmonic exhaustion function $φ$. As a generalization of Y. Tiba's result, we prove that any holomorphic function on a connected open neighborhood of the support of $(i\partial \bar \partial φ)^{n-2}$ in $Ω$ can be extended to the whole domain $Ω$. To prove it, we combine an $L^2$ version of Serre duality and Donnelly-Fefferman type estimates on $(n,n-1)$- and $(n,n)$- forms.

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Seungjae Lee, Yoshikazu Nagata. 2019-05-14. An extension theorem of holomorphic functions on hyperconvex domains. https://arxiv.org/abs/1811.06438

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