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On the third gap for proper holomorphic maps between balls

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Abstract

Let \(F\) be a proper rational map from the complex ball \(\mathbb B ^n\) into \(\mathbb B ^N\) with \(n>7\) and \(3n+1 \le N\le 4n-7\). Then \(F\) is equivalent to a map \((G, 0, \dots , 0)\) where \(G\) is a proper holomorphic map from \(\mathbb B ^n\) into \(\mathbb B ^{3n}\).

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Acknowledgments

The major part of the paper was completed when the first two authors were visiting the School of Mathematics and Statistics, Wuhan University, in the summer of 2009. These two authors would like to express their gratitude to this institute for the hospitality during this visit.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Hubei, 430072, China

    Xiaojun Huang & Wanke Yin

  2. Department of Mathematics, Rutgers University, New Brunswick, NJ, 08903, USA

    Xiaojun Huang

  3. Department of Mathematics, University of Houston, Houston, TX, 77204, USA

    Shanyu Ji

  4. Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, Saint-Etienne-du-Rouvray, 76801, France

    Wanke Yin

Authors
  1. Xiaojun Huang
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  2. Shanyu Ji
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Correspondence to Xiaojun Huang.

Additional information

Xiaojun Huang is Supported in part by DMS-1101481.

Wanke Yin is Supported in part by FANEDD-201117, ANR-09-BLAN-0422, RFDP-20090141120010, NSFC-10901123 and NSFC-11271291.

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Huang, X., Ji, S. & Yin, W. On the third gap for proper holomorphic maps between balls. Math. Ann. 358, 115–142 (2014). https://doi.org/10.1007/s00208-013-0952-z

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  • DOI: https://doi.org/10.1007/s00208-013-0952-z

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