Higher-order geometric flow of hypersurfaces in a Riemannian manifold

doi:10.1142/S0129167X19400056

CSpace

	Higher-order geometric flow of hypersurfaces in a Riemannian manifold
	Jia, Zonglin 1; Wang, Youde 2,3,4
	2019-12-01
发表期刊	INTERNATIONAL JOURNAL OF MATHEMATICS
ISSN	0129-167X
卷号	30 期号:13 页码:47
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.
关键词	Universal interpolation inequality gradient flow Sobolev inequality on submanifold
DOI	10.1142/S0129167X19400056
收录类别	SCI
语种	英语
资助项目	NSFC[11731001]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000503464900006
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50499
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.Guangzhou Univ, Coll Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China 3.Chinese Acad Sci, AMSS, Inst Math, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Beijing, 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.