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On a Hyperconvex Manifold Without Non-constant Bounded Holomorphic Functions

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Geometric Complex Analysis

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 246))

Abstract

An example is given of a hyperconvex manifold without non-constant bounded holomorphic functions, which is realized as a domain with real-analytic Levi-flat boundary in a projective surface.

Dedicated to Professor Kang-Tae Kim on the occasion of his 60th birthday.

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Acknowledgements

The author is grateful to Kang-Tae Kim, who explained him the notion of parabolic manifold when he was a postdoc at SRC-GAIA, which is supported by an NRF grant 2011-0030044 of the Ministry of Education, the Republic of Korea. This work was also supported by JSPS KAKENHI Grant Numbers 26800057 and 18K13422.

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Authors and Affiliations

  1. Faculty of Science, Department of Mathematics, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka, 422-8529, Japan

    Masanori Adachi

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  1. Masanori Adachi
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Correspondence to Masanori Adachi .

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Editors and Affiliations

  1. Department of Mathematics Education, Kyungnam University, Changwon, Korea (Republic of)

    Jisoo Byun

  2. Department of Mathematics, Pusan National University, Busan, Korea (Republic of)

    Hong Rae Cho

  3. Center for Mathematical Challenges, Korea Institute for Advanced Study, Seoul, Korea (Republic of)

    Sung Yeon Kim

  4. Department of Mathematics, Gyeongsang National University, Jinju, Korea (Republic of)

    Kang-Hyurk Lee

  5. Department of Mathematics, Kyung Hee University, Seoul, Korea (Republic of)

    Jong-Do Park

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Adachi, M. (2018). On a Hyperconvex Manifold Without Non-constant Bounded Holomorphic Functions. In: Byun, J., Cho, H., Kim, S., Lee, KH., Park, JD. (eds) Geometric Complex Analysis. Springer Proceedings in Mathematics & Statistics, vol 246. Springer, Singapore. https://doi.org/10.1007/978-981-13-1672-2_1

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