Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On global rigidity of the $p$-th root embedding
HTML articles powered by AMS MathViewer

by Shan Tai Chan PDF
Proc. Amer. Math. Soc. 144 (2016), 347-358 Request permission


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.
  • Carlos A. Berenstein and Roger Gay, Complex variables, Graduate Texts in Mathematics, vol. 125, Springer-Verlag, New York, 1991. An introduction. MR 1107514, DOI 10.1007/978-1-4612-3024-3
  • Otto Forster, Lectures on Riemann surfaces, Graduate Texts in Mathematics, vol. 81, Springer-Verlag, New York-Berlin, 1981. Translated from the German by Bruce Gilligan. MR 648106
  • Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. MR 507725
  • John B. Conway, Functions of one complex variable, 2nd ed., Graduate Texts in Mathematics, vol. 11, Springer-Verlag, New York-Berlin, 1978. MR 503901
  • Steven G. Krantz and Harold R. Parks, A primer of real analytic functions, 2nd ed., Birkhäuser Advanced Texts: Basler LehrbĂĽcher. [Birkhäuser Advanced Texts: Basel Textbooks], Birkhäuser Boston, Inc., Boston, MA, 2002. MR 1916029, DOI 10.1007/978-0-8176-8134-0
  • Ngaiming Mok, Extension of germs of holomorphic isometries up to normalizing constants with respect to the Bergman metric, J. Eur. Math. Soc. (JEMS) 14 (2012), no. 5, 1617–1656. MR 2966662, DOI 10.4171/JEMS/343
  • Ngaiming Mok, Geometry of holomorphic isometries and related maps between bounded domains, Geometry and analysis. No. 2, Adv. Lect. Math. (ALM), vol. 18, Int. Press, Somerville, MA, 2011, pp. 225–270. MR 2882446
  • Sui-Chung Ng, On holomorphic isometric embeddings of the unit disk into polydisks, Proc. Amer. Math. Soc. 138 (2010), no. 8, 2907–2922. MR 2644903, DOI 10.1090/S0002-9939-10-10305-0
  • Sui-Chung Ng, On Holomorphic Isometric Embeddings from the Unit Disk into Polydisks and Their Generalizations, Thesis at the University of Hong Kong, 2008.
  • Makoto Namba, Branched coverings and algebraic functions, Pitman Research Notes in Mathematics Series, vol. 161, Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1987. MR 933557
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53C35, 53C55
  • Retrieve articles in all journals with MSC (2010): 53C35, 53C55
Additional Information
  • Shan Tai Chan
  • Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
  • MR Author ID: 1132275
  • Email:
  • 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:
  • MathSciNet review: 3415601