A Note on Characterizing Pluriharmonic Functions via the Ohsawa–Takegoshi Extension Theorem
Vol. 30 (2023), No. 3, Page 365–369.
Inayama, Takahiro
A Note on Characterizing Pluriharmonic Functions via the Ohsawa–Takegoshi Extension Theorem
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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.
Keywords: Ohsawa–Takegoshi extension theorem, $L^2$-extension, plurisubharmonic function, pluriharmonic function, $L^2$-extension index.
Mathematics Subject Classification (2020): 32A10, 32A36.
Received: 2023-07-06
