The extension of holomorphic functions on a non-pluriharmonic locus

2017/06/05 by Yusaku Tiba, Tiba, Yusaku
Mathematics · #32A10 #32U10 #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1706.01441

openalex publication_date 2017/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let n ≥ 4 and let Ω be a bounded hyperconvex domain in ℂⁿ. Let φ be a negative exhaustive smooth plurisubharmonic function on Ω. We show that any holomorphic function defined on a connected open neighborhood of the support of (i∂ ∂φ)^n-3 can be extended to the holomorphic function on Ω.

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