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arXiv · 2307.02048

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

Takahiro Inayama
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Abstract

For a continuous function, we prove that the function is pluriharmonic if and only if the equality part of the optimal Ohsawa--Takegoshi $L^2$-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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Takahiro Inayama. 2023-07-05. A note on characterizing pluriharmonic functions via the Ohsawa--Takegoshi extension theorem. https://arxiv.org/abs/2307.02048

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