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On global rigidity of the $ p$-th root embedding


Author: Shan Tai Chan
Journal: Proc. Amer. Math. Soc. 144 (2016), 347-358
MSC (2010): Primary 53C35, 53C55
DOI: https://doi.org/10.1090/proc/12674
Published electronically: June 9, 2015
MathSciNet review: 3415601
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Abstract: We study bona fide holomorphic isometric embeddings of the unit disk $ \Delta $ into polydisks $ \Delta ^p$ ($ p\ge 2$) with sheeting number equal to $ p$ and the assumption that all component functions of such embeddings are non-constant. We prove that all such embeddings are congruent to the $ p$-th root embedding.


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Additional Information

Shan Tai Chan
Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Email: puremath.stschan@gmail.com

DOI: https://doi.org/10.1090/proc/12674
Received by editor(s): August 13, 2014
Received by editor(s) in revised form: October 29, 2014, November 3, 2014, November 6, 2014, and November 14, 2014
Published electronically: June 9, 2015
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society