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

Mathematics

Rutgers - The State University of New Jersey, New Brunswick
University of Houston

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

16 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
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

Keywords

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

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10.4310/PAMQ.2010.v6.n3.a10

Cite this

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title = "Polynomial and rational maps between balls",

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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author = "James Faran and Xiaojun Huang and Shanyu Ji and Yuan Zhang",

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AU - Faran, James

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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IS - 3

ER -

Polynomial and rational maps between balls

Abstract

Keywords

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