KMS Of Academy of mathematics and systems sciences, CAS
| Isometric Immersions of Surfaces with Two Classes of Metrics and Negative Gauss Curvature | |
Cao, Wentao1; Huang, Feimin1,2 ; Wang, Dehua3
| |
| 2015-12-01 | |
| Source Publication | ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
 |
| ISSN | 0003-9527 |
| Volume | 218Issue:3Pages:1431-1457 |
| Abstract | 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 |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics ; Mechanics |
| WOS Subject | Mathematics, Interdisciplinary Applications ; Mechanics |
| WOS ID | WOS:000361793800007 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/20862 |
| Collection | 应用数学研究所 |
| Corresponding Author | Cao, Wentao |
| Affiliation | 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 |
| Recommended Citation 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. |
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