On holomorphic isometric embeddings of the unit disk into polydisks
HTML articles powered by AMS MathViewer
- 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.
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