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	Evolving hypersurfaces by their mean curvature in the background manifold evolving by Ricci flow
	Sheng, Weimin ; Yu, Haobin
	2017
关键词	Mean curvature flow normalized Ricci flow totally geodesic sphere RIEMANNIAN-MANIFOLDS SINGULARITIES
英文摘要	We consider the problem of deforming a one-parameter family of hypersurfaces immersed into closed Riemannian manifolds with positive curvature operator. The hypersurface in this family satisfies mean curvature flow while the ambient metric satisfying the normalized Ricci flow. We prove that if the initial background manifold is an approximation of a spherical space form and the initial hypersurface also satisfies a suitable pinching condition, then either the hypersurfaces shrink to a round point in finite time or converge to a totally geodesic sphere as the time tends to infinity.; NSFC [11131007, 11571304]; Zhejiang Provincial Natural Science Foundation of China [LY14A010019]; SCI(E); ARTICLE; 1; 19
语种	英语
出处	SCI
出版者	COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/475553]
专题	数学科学学院
推荐引用方式 GB/T 7714	Sheng, Weimin,Yu, Haobin. Evolving hypersurfaces by their mean curvature in the background manifold evolving by Ricci flow. 2017-01-01.

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