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

SAS - Mathematics

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

11 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

Mathematics(all)

Keywords

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

Access to Document

10.4310/PAMQ.2010.v6.n3.a10

Cite this

@article{56b6d0ac97034aa2a3b08e035ab11233,

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.",

keywords = "Criterion, Equivalent, Maps between balls, Polynomial maps, Proper holomorphic maps, Rational maps",

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

year = "2010",

month = jul,

doi = "10.4310/PAMQ.2010.v6.n3.a10",

language = "English (US)",

volume = "6",

pages = "829--842",

journal = "Pure and Applied Mathematics Quarterly",

issn = "1558-8599",

publisher = "International Press of Boston, Inc.",

number = "3",

}

TY - JOUR

T1 - Polynomial and rational maps between balls

AU - Faran, James

AU - Huang, Xiaojun

AU - Ji, Shanyu

AU - Zhang, Yuan

PY - 2010/7

Y1 - 2010/7

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

UR - http://www.scopus.com/inward/record.url?scp=79951971053&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79951971053&partnerID=8YFLogxK

U2 - 10.4310/PAMQ.2010.v6.n3.a10

DO - 10.4310/PAMQ.2010.v6.n3.a10

M3 - Article

AN - SCOPUS:79951971053

VL - 6

SP - 829

EP - 842

JO - Pure and Applied Mathematics Quarterly

JF - Pure and Applied Mathematics Quarterly

SN - 1558-8599

IS - 3

ER -

Polynomial and rational maps between balls

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this