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Classification of Proper Holomorphic Mappings Between Generalized Pseudoellipsoids of Different Dimensions

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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 give a rigidity theorem of proper holomorphic mappings between generalized pseudoellipsoids. The theorem claims that any proper holomorphic mapping which is holomorphic extendable up to the boundary between generalized pseudoellipsoids of non-equidimensions is a collections of totally geodesic embeddings up to automorphisms.

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Authors and Affiliations

  1. 716 Tokuma, Nagano, 381-8550, Japan

    Atsushi Hayashimoto

Authors
  1. Atsushi Hayashimoto
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Corresponding author

Correspondence to Atsushi Hayashimoto .

Editor information

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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Hayashimoto, A. (2015). Classification of Proper Holomorphic Mappings Between Generalized Pseudoellipsoids of Different Dimensions. 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_10

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