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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.

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On holomorphic isometric embeddings of the unit disk into polydisks
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by Sui-Chung Ng PDF
Proc. Amer. Math. Soc. 138 (2010), 2907-2922 Request permission

Abstract:

We study the classification of holomorphic isometric embeddings of the unit disk into polydisks. As a corollary of our results, we can give a complete classification when the target is the 2-disk and the 3-disk. We also prove that the holomorphic isometric embeddings between polydisks are induced by those of the unit disk into polydisks.
References
  • Eugenio Calabi, Isometric imbedding of complex manifolds, Ann. of Math. (2) 58 (1953), 1–23. MR 57000, DOI 10.2307/1969817
  • Laurent Clozel and Emmanuel Ullmo, Correspondances modulaires et mesures invariantes, J. Reine Angew. Math. 558 (2003), 47–83 (French). MR 1979182, DOI 10.1515/crll.2003.042
  • Mok, N., Erratum to “Local holomorphic isometric embeddings arising from correspondences in the rank-$1$ case”, 2005, http://hkumath.hku.hk/$\sim$nmok/Erratum.pdf.
  • Ngaiming Mok, Local holomorphic isometric embeddings arising from correspondences in the rank-1 case, Contemporary trends in algebraic geometry and algebraic topology (Tianjin, 2000) Nankai Tracts Math., vol. 5, World Sci. Publ., River Edge, NJ, 2002, pp. 155–165. MR 1945359, DOI 10.1142/9789812777416_{0}007
  • —, Extension of germs of holomorphic isometries up to normalization constants with respect to the Bergman metric, preprint, http://hkumath.hku.hk/$\sim$imr/IMRPreprintSeries/2009/IMR2009-9.pdf.
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Additional Information
  • Sui-Chung Ng
  • Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
  • Email: math.scng@hku.hk
  • Received by editor(s): July 30, 2009
  • Received by editor(s) in revised form: November 27, 2009
  • Published electronically: March 19, 2010
  • Communicated by: Richard A. Wentworth
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 2907-2922
  • MSC (2010): Primary 53C35, 53C55
  • DOI: https://doi.org/10.1090/S0002-9939-10-10305-0
  • MathSciNet review: 2644903