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The Schwarz Lemma at the Boundary of the Non-Convex Complex Ellipsoids

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Abstract

Let B2,p:= {z ∈ ℂ2: ∣z1∣2+ ∣z2∣p < 1} (0 < p< 1). Then, B2,p(0 < p < 1) is a non-convex complex ellipsoid in ℂ2 without smooth boundary. In this article, we establish a boundary Schwarz lemma at z0 ∈ ∂B2,p for holomorphic self-mappings of the non-convex complex ellipsoid B2, p, where z0 is any smooth boundary point of B2,p.

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Authors and Affiliations

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

    Le He  (何乐) & Zhenhan Tu  (涂振汊)

Authors
  1. Le He  (何乐)
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  2. Zhenhan Tu  (涂振汊)
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Correspondence to Zhenhan Tu  (涂振汊).

Additional information

The project supported in part by the National Natural Science Foundation of China (11671306).

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He, L., Tu, Z. The Schwarz Lemma at the Boundary of the Non-Convex Complex Ellipsoids. Acta Math Sci 39, 915–926 (2019). https://doi.org/10.1007/s10473-019-0401-5

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  • DOI: https://doi.org/10.1007/s10473-019-0401-5

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