Compactness of Surfaces in R-n with Small Total Curvature
文献类型：期刊论文
| 作者 | Sun, Jianxin1; Zhou, Jie2 |
| 刊名 | JOURNAL OF GEOMETRIC ANALYSIS
 |
| 出版日期 | 2021-02-05 |
| 页码 | 33 |
| 关键词 | Isothermal radius Compactness Bi-Lipschitz parametrization Total curvature |
| ISSN号 | 1050-6926 |
| DOI | 10.1007/s12220-020-00583-z |
| 英文摘要 | In this paper, we study the compactness and local structure of immersed surfaces in the unit ball of R-n with uniformly bounded area and small total curvature. A key ingredient is a new quantity we call isothermal radius. By estimating the lower bound of the isothermal radius, we establish a compactness theorem of such surfaces in intrinsic L-p-topology and extrinsic W-2,W-2-weak topology. As applications, we get bi-Lipschitz parametrization of such surfaces, explain Leon Simon's decomposition theorem (Simon in Commun Anal Geom 1(2):281-326, 1993) in the viewpoint of convergence and prove a non-collapsing version of Helein's convergence theorem (Helein in Harmonicmaps, conservation laws and moving frames, Cambridge University Press, Cambridge, 2002; Kuwert and Li in Commun Anal Geom 20(2):313-340, 2012). |
| 资助项目 | NSFC[11721101] ; National Key Research and Development Project[SQ2020YFA070080] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000615143200002 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/58176]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Zhou, Jie |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China |
| 推荐引用方式 GB/T 7714 | Sun, Jianxin,Zhou, Jie. Compactness of Surfaces in R-n with Small Total Curvature[J]. JOURNAL OF GEOMETRIC ANALYSIS,2021:33. |
| APA | Sun, Jianxin,&Zhou, Jie.(2021).Compactness of Surfaces in R-n with Small Total Curvature.JOURNAL OF GEOMETRIC ANALYSIS,33. |
| MLA | Sun, Jianxin,et al."Compactness of Surfaces in R-n with Small Total Curvature".JOURNAL OF GEOMETRIC ANALYSIS (2021):33. |
入库方式： OAI收割
来源：数学与系统科学研究院
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