Proper holomorphic maps from the unit disk to some unit ball
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- by John P. D’Angelo, Zhenghui Huo and Ming Xiao PDF
- Proc. Amer. Math. Soc. 145 (2017), 2649-2660 Request permission
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 $2$.References
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Additional Information
- John P. D’Angelo
- Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801
- MR Author ID: 53760
- 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
- MR Author ID: 1198280
- Email: huo@wustl.edu
- Ming Xiao
- Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801
- MR Author ID: 904127
- Email: mingxiao@illinois.edu
- 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
- © Copyright 2016 American Mathematical Society
- 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
- MathSciNet review: 3626518