A note on characterizing pluriharmonic functions via the Ohsawa--Takegoshi extension theorem

2023/07/05 by Takahiro Inayama, Inayama, Takahiro
Mathematics · #32A10 #32A36 #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2307.02048

openalex publication_date 2023/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

For a continuous function, we prove that the function is pluriharmonic if and only if the equality part of the optimal Ohsawa--Takegoshi L²-extension theorem is satisfied with respect to the metric having the function as a weight. This partially resolves the conjecture proposed by the author.

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