GEOMETRICALLY FINITE AND SEMI-RATIONAL BRANCHED COVERINGS OF THE TWO-SPHERE

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	GEOMETRICALLY FINITE AND SEMI-RATIONAL BRANCHED COVERINGS OF THE TWO-SPHERE
	Cui, Guizhen1 ; Jiang, Yunping 2,3
	2011-05-01
发表期刊	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN	0002-9947
卷号	363 期号:5 页码:2701-2714
摘要	In 1982, Thurston gave a necessary and sufficient condition for a critically finite branched covering of the two-sphere to itself to be combinatorially equivalent to a rational map. We discuss extending this result to geometrically finite rational maps. We give an example to show that Thurston's original condition is not sufficient. This example is topologically pathological near accumulation points of the postcritical set. We give two conditions forbidding such pathology, show that they are equivalent, and (in a sequel to the present paper) will show that Thurston's condition together with this tameness is both necessary and sufficient to characterize geometrically finite rational maps.
关键词	Geometrically finite branched covering semi-rational branched covering sub-hyperbolic semi-rational branched covering
语种	英语
资助项目	NSF ; PSC-CUNY ; NSFC[10831004] ; BaiRenJiHu
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000290511300017
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11937
专题	数学所
通讯作者	Cui, Guizhen
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.CUNY, Dept Math, Queens Coll, Flushing, NY 11367 USA 3.CUNY Grad Ctr, Dept Math, New York, NY 10016 USA
推荐引用方式 GB/T 7714	Cui, Guizhen,Jiang, Yunping. GEOMETRICALLY FINITE AND SEMI-RATIONAL BRANCHED COVERINGS OF THE TWO-SPHERE[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2011,363(5):2701-2714.
APA	Cui, Guizhen,&Jiang, Yunping.(2011).GEOMETRICALLY FINITE AND SEMI-RATIONAL BRANCHED COVERINGS OF THE TWO-SPHERE.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,363(5),2701-2714.
MLA	Cui, Guizhen,et al."GEOMETRICALLY FINITE AND SEMI-RATIONAL BRANCHED COVERINGS OF THE TWO-SPHERE".TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 363.5(2011):2701-2714.