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Holomorphic isometric maps from the complex unit ball to reducible bounded symmetric domains

  • Ming Xiao EMAIL logo
Published/Copyright: June 25, 2022

Abstract

The first part of the paper studies the boundary behavior of holomorphic isometric mappings F=(F1,,Fm) from the complex unit ball 𝔹n, n2, to a bounded symmetric domain Ω=Ω1××Ωm up to constant conformal factors, where Ωis are irreducible factors of Ω. We prove every non-constant component Fi must map generic boundary points of 𝔹n to the boundary of Ωi. In the second part of the paper, we establish a rigidity result for local holomorphic isometric maps from the unit ball to a product of unit balls and Lie balls.

Award Identifier / Grant number: DMS-1800549

Award Identifier / Grant number: DMS-2045104

Funding statement: Supported in part by NSF grant DMS-1800549 and DMS-2045104.

Acknowledgements

The author thanks Yuan Yuan for helpful comments. The author is grateful to the anonymous referees for valuable comments that help improve the exposition of the paper.

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Received: 2021-10-14
Revised: 2022-04-04
Published Online: 2022-06-25
Published in Print: 2022-08-01

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