Journal of the Mathematical Society of Japan

A characterization of regular points by Ohsawa–Takegoshi extension theorem

Qi'an GUAN and Zhenqian LI

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In this article, we present that the germ of a complex analytic set at the origin in $\mathbb{C}^n$ is regular if and only if the related Ohsawa–Takegoshi extension theorem holds. We also obtain a necessary condition of the $L^2$ extension of bounded holomorphic sections from singular analytic sets.

Article information

J. Math. Soc. Japan, Volume 70, Number 1 (2018), 403-408.

First available in Project Euclid: 26 January 2018

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Zentralblatt MATH identifier

Primary: 32C30: Integration on analytic sets and spaces, currents {For local theory, see 32A25 or 32A27} 32C35: Analytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30] 32U05: Plurisubharmonic functions and generalizations [See also 31C10]

Ohsawa–Takegoshi extension theorem plurisubharmonic function integral closure of ideals


GUAN, Qi'an; LI, Zhenqian. A characterization of regular points by Ohsawa–Takegoshi extension theorem. J. Math. Soc. Japan 70 (2018), no. 1, 403--408. doi:10.2969/jmsj/07017560.

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