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Functions Holomorphic Along a \(C^1\) Pencil of Holomorphic Discs

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Abstract

The main purpose of this article is to present a generalization of Forelli’s theorem for the functions holomorphic along a general pencil of holomorphic discs. This generalizes the main result of Joo et al. (Math Ann 355(3):1171–1176, 2013) and the original Forelli’s theorem, and furthermore, answers one of the problems posed in Chirka (Proc Steklov Inst Math 253(2):212–220, 2006).

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  1. Department of Mathematics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea

    Ye-Won Luke Cho & Kang-Tae Kim

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  1. Ye-Won Luke Cho
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  2. Kang-Tae Kim
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Correspondence to Kang-Tae Kim.

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Research of the authors is supported in part by NRF Grant 4.0019528 of The Republic of Korea (South)

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Cho, YW.L., Kim, KT. Functions Holomorphic Along a \(C^1\) Pencil of Holomorphic Discs. J Geom Anal 31, 10634–10647 (2021). https://doi.org/10.1007/s12220-021-00660-x

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