An extension theorem of holomorphic functions on hyperconvex domains

2018/11/15 by Lee, Seungjae, Nagata, Yoshikazu
#32A10 #32D15 #32U10 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.06438

Abstract

Let n ≥ 3 and Ω be a bounded domain in ℂⁿ 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∂ ∂ φ)^n-2 in Ω can be extended to the whole domain Ω. To prove it, we combine an L² version of Serre duality and Donnelly-Fefferman type estimates on (n,n-1)- and (n,n)- forms.

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