Isometric Immersions of Surfaces with Two Classes of Metrics and Negative Gauss Curvature

doi:10.1007/s00205-015-0885-7

CSpace > 应用数学研究所

	Isometric Immersions of Surfaces with Two Classes of Metrics and Negative Gauss Curvature
	Cao, Wentao 1; Huang, Feimin1,2 ; Wang, Dehua 3
	2015-12-01
发表期刊	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN	0003-9527
卷号	218 期号:3 页码:1431-1457
摘要	The isometric immersion of two-dimensional Riemannian manifolds or surfaces with negative Gauss curvature into the three-dimensional Euclidean space is studied in this paper. The global weak solutions to the Gauss-Codazzi equations with large data in are obtained through the vanishing viscosity method and the compensated compactness framework. The uniform estimate and H (-1) compactness are established through a transformation of state variables and construction of proper invariant regions for two types of given metrics including the catenoid type and the helicoid type. The global weak solutions in to the Gauss-Codazzi equations yield the C (1,1) isometric immersions of surfaces with the given metrics.
DOI	10.1007/s00205-015-0885-7
语种	英语
资助项目	NSFC[11371349] ; NSFC[11328102] ; National Basic Research Program of China (973 Program)[2011CB808002] ; CAS Program for Cross and Cooperative Team of the Science and Technology Innovation ; NSF[DMS-1312800]
WOS研究方向	Mathematics ; Mechanics
WOS类目	Mathematics, Interdisciplinary Applications ; Mechanics
WOS记录号	WOS:000361793800007
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/20862
专题	应用数学研究所
通讯作者	Cao, Wentao
作者单位	1.Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China 2.Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China 3.Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
推荐引用方式 GB/T 7714	Cao, Wentao,Huang, Feimin,Wang, Dehua. Isometric Immersions of Surfaces with Two Classes of Metrics and Negative Gauss Curvature[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2015,218(3):1431-1457.
APA	Cao, Wentao,Huang, Feimin,&Wang, Dehua.(2015).Isometric Immersions of Surfaces with Two Classes of Metrics and Negative Gauss Curvature.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,218(3),1431-1457.
MLA	Cao, Wentao,et al."Isometric Immersions of Surfaces with Two Classes of Metrics and Negative Gauss Curvature".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 218.3(2015):1431-1457.