On a Rigidity Problem of Beardon and Minda | |
L, Baokui3,4; Wang, Yuefei1,2 | |
刊名 | COMPUTATIONAL METHODS AND FUNCTION THEORY |
2021-06-17 | |
页码 | 9 |
关键词 | Cross-ratios Absolute cross-ratios Mobius transformations Conjugate Mobius transformations |
ISSN号 | 1617-9447 |
DOI | 10.1007/s40315-021-00393-6 |
英文摘要 | 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. |
资助项目 | NSF of China[11688101] |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | SPRINGER HEIDELBERG |
WOS记录号 | WOS:000662797700001 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/58863] |
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.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China 2.Shenzhen Univ, Coll Math & Stat, Shenzhen 518060, Guandong, Peoples R China 3.Beijing Inst Technol, Beijing Key Lab MCAACI, Beijing 100081, Peoples R China 4.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, 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. |
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