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Proper holomorphic maps from the unit disk to some unit ball


Authors: John P. D’Angelo, Zhenghui Huo and Ming Xiao
Journal: Proc. Amer. Math. Soc. 145 (2017), 2649-2660
MSC (2010): Primary 32H35, 51F25, 32M99; Secondary 30J99
DOI: https://doi.org/10.1090/proc/13425
Published electronically: December 8, 2016
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Abstract: We study proper rational maps from the unit disk to balls in higher dimensions. After gathering some known results, we study the moduli space of unitary equivalence classes of polynomial proper maps from the disk to a ball, and we establish a normal form for these equivalence classes. We also prove that all rational proper maps from the disk to a ball are homotopic in target dimension at least $ 2$.


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Additional Information

John P. D’Angelo
Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801
Email: jpda@math.uiuc.edu

Zhenghui Huo
Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801
Address at time of publication: Department of Mathematics, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130-4899
Email: huo@wustl.edu

Ming Xiao
Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801
Email: mingxiao@illinois.edu

DOI: https://doi.org/10.1090/proc/13425
Keywords: Proper holomorphic mappings, unit disk, unit ball, unitary equivalence, homotopy equivalence
Received by editor(s): June 6, 2016
Received by editor(s) in revised form: August 1, 2016
Published electronically: December 8, 2016
Communicated by: Franc Forstneric
Article copyright: © Copyright 2016 American Mathematical Society