Polynomial and rational maps between balls

James Faran; Xiaojun Huang; Shanyu Ji; Yuan Zhang

doi:10.4310/PAMQ.2010.v6.n3.a10

Polynomial and rational maps between balls

James Faran, Xiaojun Huang, Shanyu Ji, Yuan Zhang

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

For a proper holomorphic map F from a ball Bⁿ into another ball B^N, we give a criterion when a rational map F is equivalent to a polynomial one. As application, we show that proper rational holomorphic maps from B² into B^N of degree two are equivalent to polynomial maps, and we also give an example of a rational holomorphic maps of degree 3 that are 'almost' linear but are not equivalent to holomorphic polynomial maps.

Original language	English (US)
Pages (from-to)	829-842
Number of pages	14
Journal	Pure and Applied Mathematics Quarterly
Volume	6
Issue number	3
DOIs	https://doi.org/10.4310/PAMQ.2010.v6.n3.a10
State	Published - Jul 2010

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Criterion
Equivalent
Maps between balls
Polynomial maps
Proper holomorphic maps
Rational maps

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10.4310/PAMQ.2010.v6.n3.a10

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abstract = "For a proper holomorphic map F from a ball Bn into another ball BN, we give a criterion when a rational map F is equivalent to a polynomial one. As application, we show that proper rational holomorphic maps from B2 into BN of degree two are equivalent to polynomial maps, and we also give an example of a rational holomorphic maps of degree 3 that are 'almost' linear but are not equivalent to holomorphic polynomial maps.",

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AU - Huang, Xiaojun

AU - Ji, Shanyu

AU - Zhang, Yuan

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N2 - For a proper holomorphic map F from a ball Bn into another ball BN, we give a criterion when a rational map F is equivalent to a polynomial one. As application, we show that proper rational holomorphic maps from B2 into BN of degree two are equivalent to polynomial maps, and we also give an example of a rational holomorphic maps of degree 3 that are 'almost' linear but are not equivalent to holomorphic polynomial maps.

AB - For a proper holomorphic map F from a ball Bn into another ball BN, we give a criterion when a rational map F is equivalent to a polynomial one. As application, we show that proper rational holomorphic maps from B2 into BN of degree two are equivalent to polynomial maps, and we also give an example of a rational holomorphic maps of degree 3 that are 'almost' linear but are not equivalent to holomorphic polynomial maps.

KW - Criterion

KW - Equivalent

KW - Maps between balls

KW - Polynomial maps

KW - Proper holomorphic maps

KW - Rational maps

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Polynomial and rational maps between balls

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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