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D’Angelo conjecture in the third gap interval

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Abstract

We show that the D’Angelo conjecture holds in the third gap interval. More precisely, we prove that the degree of any rational proper holomorphic map from \({\mathbb {B}}^n\) to \({\mathbb {B}}^{4n-6}\) with \(n\ge 7\) is not more than 3.

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Acknowledgements

The authors would like to thank Xiaojun Huang for helpful discussions. The authors are also indebted to the referee for many very useful suggestions and comments.

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Authors and Affiliations

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

    Shanyu Ji

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

    Wanke Yin

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  1. Shanyu Ji
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  2. Wanke Yin
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Correspondence to Wanke Yin.

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The second author is supported in part by NSFC-11722110 and NSFC-11571260.

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Ji, S., Yin, W. D’Angelo conjecture in the third gap interval. Math. Z. 295, 1583–1595 (2020). https://doi.org/10.1007/s00209-019-02428-0

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