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Higher-order geometric flow of hypersurfaces in a Riemannian manifold

文献类型：期刊论文

作者Jia, Zonglin1; Wang, Youde2,3,4
刊名INTERNATIONAL JOURNAL OF MATHEMATICS
出版日期2019-12-01
卷号30期号:13页码:47
关键词Universal interpolation inequality gradient flow Sobolev inequality on submanifold
ISSN号0129-167X
DOI10.1142/S0129167X19400056
英文摘要In this paper, we consider the high-order geometric flows of a compact submanifolds M in a complete Riemannian manifold N with dim(N) = dim(M) + 1 = n + 1, which were introduced by Mantegazza in the case the ambient space is an Euclidean space, and extend some results due to Mantegazza to the present situation under some assumptions on N. Precisely, we show that if m is an element of N is strictly larger than the integer part of n/2 and phi(t) is an immersion for all t is an element of [0, T) and if F-m(phi(0)) is bounded by a constant which relies on the injectivity radius (R) over bar> 0 and sectional curvature (K) over bar (pi) ((K) over bar (pi) <= 1) of N, then T must be infinity.
资助项目NSFC[11731001]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000503464900006
出版者WORLD SCIENTIFIC PUBL CO PTE LTD
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/50498]  
专题中国科学院数学与系统科学研究院
通讯作者Wang, Youde
作者单位1.China Acad Engn Phys, Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China
2.Univ Chinese Acad Sci, Beijing, Peoples R China
3.Chinese Acad Sci, AMSS, Inst Math, Beijing 100190, Peoples R China
4.Guangzhou Univ, Coll Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China
推荐引用方式
GB/T 7714		 Jia, Zonglin,Wang, Youde. Higher-order geometric flow of hypersurfaces in a Riemannian manifold[J]. INTERNATIONAL JOURNAL OF MATHEMATICS,2019,30(13):47.
APA Jia, Zonglin,&Wang, Youde.(2019).Higher-order geometric flow of hypersurfaces in a Riemannian manifold.INTERNATIONAL JOURNAL OF MATHEMATICS,30(13),47.
MLA Jia, Zonglin,et al."Higher-order geometric flow of hypersurfaces in a Riemannian manifold".INTERNATIONAL JOURNAL OF MATHEMATICS 30.13(2019):47.

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来源：数学与系统科学研究院

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