Mean Curvature Flow of Surface in 4-Manifolds
β Scribed by Jingyi Chen; Jiayu Li
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 187 KB
- Volume
- 163
- Category
- Article
- ISSN
- 0001-8708
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## Abstract We study the flow __M~t~__ of a smooth, strictly convex hypersurface by its mean curvature in β^__n__ + 1^. The surface remains smooth and convex, shrinking monotonically until it disappears at a critical time __T__ and point __x__^\*^ (which is due to Huisken). This is equivalent to sa
## Abstract Let __f__ be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of __f__ under various conditions. A corollary is that any areaβdecreasing map between unit spheres (of possibly differe
A submanifold M" of a Euclidean space Em is said to have harmonic mean curvature vector field if A# = a, where denotes the mern curvature vector. B. -Y. CHEN conjectured that the only submanifolds of Euclidean spaces with harmonic mean curvature vector field, are the minimal ones. In this paper, we