On a Rigidity Problem of Beardon and Minda

doi:10.1007/s40315-021-00393-6

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	On a Rigidity Problem of Beardon and Minda
	L, Baokui 1,2; Wang, Yuefei 3,4
	2021-06-17
发表期刊	COMPUTATIONAL METHODS AND FUNCTION THEORY
ISSN	1617-9447
页码	9
摘要	In this paper, we give a positive answer to a rigidity problem of maps on the Riemann sphere related to cross-ratios, posed by Beardon and Minda (Proc Am Math Soc 130(4):987-998, 2001). Our main results are: (I) Let E not subset of R be an arc or a circle. If a map f : (C) over cap bar right arrow (C) over cap preserves cross-ratios in E, then f is aMobius transformation when (E) over bar not equal E and f is a Mobius or conjugate Mobius transformation when (E) over bar = E, where (EE) over bar = {z vertical bar z is an element of E}. (II) Let E subset of (R) over cap be an arc satisfying the condition that the cardinal number #(E boolean AND{0, 1, infinity 8}) < 2. If f preserves cross-ratios in E, then f is a Mobius or conjugateMobius transformation. Examples are provided to show that the assumption #(E boolean AND {0, 1, infinity}) < 2 is necessary.
关键词	Cross-ratios Absolute cross-ratios Mobius transformations Conjugate Mobius transformations
DOI	10.1007/s40315-021-00393-6
收录类别	SCI
语种	英语
资助项目	NSF of China[11688101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000662797700001
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58864
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Yuefei
作者单位	1.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China 2.Beijing Inst Technol, Beijing Key Lab MCAACI, Beijing 100081, Peoples R China 3.Shenzhen Univ, Coll Math & Stat, Shenzhen 518060, Guandong, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	L, Baokui,Wang, Yuefei. On a Rigidity Problem of Beardon and Minda[J]. COMPUTATIONAL METHODS AND FUNCTION THEORY,2021:9.
APA	L, Baokui,&Wang, Yuefei.(2021).On a Rigidity Problem of Beardon and Minda.COMPUTATIONAL METHODS AND FUNCTION THEORY,9.
MLA	L, Baokui,et al."On a Rigidity Problem of Beardon and Minda".COMPUTATIONAL METHODS AND FUNCTION THEORY (2021):9.