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November 2017 Classification Problem of Holomorphic Isometries of the Unit Disk Into Polydisks
Shan Tai Chan
Michigan Math. J. 66(4): 745-767 (November 2017). DOI: 10.1307/mmj/1505527453

Abstract

We study the classification problem of holomorphic isometric embeddings of the unit disk into polydisks as in [Ng10, Ch16a]. We give a complete classification of all such holomorphic isometries when the target is the 4-disk Δ4. Moreover, we classify those holomorphic isometric embeddings with certain prescribed sheeting numbers. In addition, we prove that a known example in the space HIk(Δ,Δqk;q) is globally rigid for any integers k,q2, which generalizes Theorem 1.1 in [Ch16a].

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Shan Tai Chan. "Classification Problem of Holomorphic Isometries of the Unit Disk Into Polydisks." Michigan Math. J. 66 (4) 745 - 767, November 2017. https://doi.org/10.1307/mmj/1505527453

Information

Received: 27 May 2016; Revised: 13 June 2017; Published: November 2017
First available in Project Euclid: 16 September 2017

zbMATH: 06822184
MathSciNet: MR3720322
Digital Object Identifier: 10.1307/mmj/1505527453

Subjects:
Primary: 30B40, 30F45, 32H02, 53C55

Rights: Copyright © 2017 The University of Michigan

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Vol.66 • No. 4 • November 2017
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