Compactness of Surfaces in R-n with Small Total Curvature

doi:10.1007/s12220-020-00583-z

CSpace

	Compactness of Surfaces in R-n with Small Total Curvature
	Sun, Jianxin 1; Zhou, Jie 2
	2021-02-05
发表期刊	JOURNAL OF GEOMETRIC ANALYSIS
ISSN	1050-6926
页码	33
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).
关键词	Isothermal radius Compactness Bi-Lipschitz parametrization Total curvature
DOI	10.1007/s12220-020-00583-z
收录类别	SCI
语种	英语
资助项目	NSFC[11721101] ; National Key Research and Development Project[SQ2020YFA070080]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000615143200002
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58177
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.