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Compact Smooth but Non-complex Complements of Complete Kähler Manifolds

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Complex Analysis and Geometry

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 144))

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Abstract

We modify the techniques developed by Diederich and Fornaess, and construct compact smooth submanifolds of arbitrary real codimension \(\ge 3\), which are non-complex as the complements of complete Kähler manifolds.

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References

  1. Anchouche, B.: Analyticity of compact complements of complete Kähler manifolds. Proc. AMS 137, 3037–3044 (2009)

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  2. Diederich, K., Fornaess, J.E.: Thin complements of complete Kähler domains. Math. Ann. 259, 331–341 (1982)

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Acknowledgments

I would like to thank Professor Nikolay V. Shcherbina for pointing out Edlund’s result and for helpful discussion during KSCV 10.

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Authors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, 464-8602, Nagoya, Japan

    Xu Liu

Authors
  1. Xu Liu
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Correspondence to Xu Liu .

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Editors and Affiliations

  1. Department of Mathematics, Università di Roma Tor Vergata, Rome, Italy

    Filippo Bracci

  2. Dept. of Mathematics Education, Kyungnam University, Changwon, Korea (Republic of)

    Jisoo Byun

  3. Université Joseph Fourier Grenoble, Institut Fourier, Grenoble, France

    Hervé Gaussier

  4. Graduate School of Mathematical Sciences, The University of Tokyo, Meguro-ku, Tokyo, Japan

    Kengo Hirachi

  5. Department of Mathematics, POSTECH, Pohang, Korea (Republic of)

    Kang-Tae Kim

  6. Department of Mathematics, Bergische Universität Wuppertal, Wuppertal, Nordrhein-Westfalen, Germany

    Nikolay Shcherbina

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Liu, X. (2015). Compact Smooth but Non-complex Complements of Complete Kähler Manifolds. In: Bracci, F., Byun, J., Gaussier, H., Hirachi, K., Kim, KT., Shcherbina, N. (eds) Complex Analysis and Geometry. Springer Proceedings in Mathematics & Statistics, vol 144. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55744-9_17

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