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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On global rigidity of the $p$-th root embedding
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by Shan Tai Chan PDF
Proc. Amer. Math. Soc. 144 (2016), 347-358 Request permission

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
  • MR Author ID: 1132275
  • Email: puremath.stschan@gmail.com
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 347-358
  • MSC (2010): Primary 53C35, 53C55
  • DOI: https://doi.org/10.1090/proc/12674
  • MathSciNet review: 3415601