Minimal Submanifolds and Related Topics最新文献

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Bernstein Type Theorems for Higher Codimension 高余维的Bernstein型定理
Minimal Submanifolds and Related Topics Pub Date : 2018-07-30 DOI: 10.1142/9789813236066_0008
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引用次数: 3
Intrinsic Rigidity Theorems 固有刚性定理
Minimal Submanifolds and Related Topics Pub Date : 2018-07-30 DOI: 10.1142/9789813236066_0005
{"title":"Intrinsic Rigidity Theorems","authors":"","doi":"10.1142/9789813236066_0005","DOIUrl":"https://doi.org/10.1142/9789813236066_0005","url":null,"abstract":"","PeriodicalId":162832,"journal":{"name":"Minimal Submanifolds and Related Topics","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126689274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stable Minimal Hypersurfaces 稳定极小超曲面
Minimal Submanifolds and Related Topics Pub Date : 2018-07-30 DOI: 10.1142/9789812564382_0006
Y. Xin
{"title":"Stable Minimal Hypersurfaces","authors":"Y. Xin","doi":"10.1142/9789812564382_0006","DOIUrl":"https://doi.org/10.1142/9789812564382_0006","url":null,"abstract":"","PeriodicalId":162832,"journal":{"name":"Minimal Submanifolds and Related Topics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133692700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Minimal Submanifolds of Higher Codimension 高余维的极小子流形
Minimal Submanifolds and Related Topics Pub Date : 2018-07-30 DOI: 10.1142/9789813236066_0007
R. Schoen
{"title":"Minimal Submanifolds of Higher Codimension","authors":"R. Schoen","doi":"10.1142/9789813236066_0007","DOIUrl":"https://doi.org/10.1142/9789813236066_0007","url":null,"abstract":"In this series of lectures we will introduce methods for handling problems in Riemannian geometry involving curvature. These methods are especially effective in handling positive curvature, but they also motivate questions for minimal submanifolds in euclidean space. The theory of minimal hypersurfaces is particularly important for positive scalar curvature including questions in General Relativity (see [25] for a survey of this topic). Much of this paper concerns the second variation and variational existence questions in arbitrary codimension. In Section 2 we introduce the basic ideas and consider questions involving sectional curvature and geodesics. We illustrate how lower estimates on the Morse index may be combined with existence theory to derive geometric conclusions. In addition to the case of closed geodesics and the fixed endpoint problem we also consider the free boundary problem for geodesics and some of its consequences. In Section 3 we consider mainly the case of surfaces in arbitrary manifolds and show how the conditions of positive complex sectional curvature and PIC arise naturally from the second variation in complex form. We note that after these lectures were given, S. Brendle and the author ([4], [5]) were able to show that PIC is preserved by the Ricci flow and as a consequence to show that positive pointwise quarter-pinched manifolds are diffeomorphic to spherical space","PeriodicalId":162832,"journal":{"name":"Minimal Submanifolds and Related Topics","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121667989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
BACK MATTER 回到问题
Minimal Submanifolds and Related Topics Pub Date : 2018-07-30 DOI: 10.1142/9789813236066_bmatter
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引用次数: 0
Bernstein’s Theorem and Its Generalizations 伯恩斯坦定理及其推广
Minimal Submanifolds and Related Topics Pub Date : 2018-07-30 DOI: 10.1142/9789813236066_0002
{"title":"Bernstein’s Theorem and Its Generalizations","authors":"","doi":"10.1142/9789813236066_0002","DOIUrl":"https://doi.org/10.1142/9789813236066_0002","url":null,"abstract":"","PeriodicalId":162832,"journal":{"name":"Minimal Submanifolds and Related Topics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128270246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
FRONT MATTER 前页
Minimal Submanifolds and Related Topics Pub Date : 2018-07-30 DOI: 10.1142/9789813236066_fmatter
{"title":"FRONT MATTER","authors":"","doi":"10.1142/9789813236066_fmatter","DOIUrl":"https://doi.org/10.1142/9789813236066_fmatter","url":null,"abstract":"","PeriodicalId":162832,"journal":{"name":"Minimal Submanifolds and Related Topics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131418137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weierstrass Type Representations weerstrass类型表示
Minimal Submanifolds and Related Topics Pub Date : 2018-07-30 DOI: 10.1142/9789813236066_0003
{"title":"Weierstrass Type Representations","authors":"","doi":"10.1142/9789813236066_0003","DOIUrl":"https://doi.org/10.1142/9789813236066_0003","url":null,"abstract":"","PeriodicalId":162832,"journal":{"name":"Minimal Submanifolds and Related Topics","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132520747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Plateau’s Problem and Douglas-Rado Solution 高原问题和道格拉斯-拉多解决方案
Minimal Submanifolds and Related Topics Pub Date : 2018-07-30 DOI: 10.1142/9789813236066_0004
{"title":"Plateau’s Problem and Douglas-Rado Solution","authors":"","doi":"10.1142/9789813236066_0004","DOIUrl":"https://doi.org/10.1142/9789813236066_0004","url":null,"abstract":"","PeriodicalId":162832,"journal":{"name":"Minimal Submanifolds and Related Topics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127656577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Entire Space-Like Submanifolds 整个类空间子流形
Minimal Submanifolds and Related Topics Pub Date : 2003-12-01 DOI: 10.1142/9789812564382_0008
Y. Xin
{"title":"Entire Space-Like Submanifolds","authors":"Y. Xin","doi":"10.1142/9789812564382_0008","DOIUrl":"https://doi.org/10.1142/9789812564382_0008","url":null,"abstract":"","PeriodicalId":162832,"journal":{"name":"Minimal Submanifolds and Related Topics","volume":"79 7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128115148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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