A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension
By Huaihuo Cao, Haizhong Li. 2011
167 citations recorded by the source corpus.
In this paper, we prove a classification theorem for self-shrinkers of the mean curvature flow with |A|2 ≤ 1 in arbitrary codimension. In particular, this implies a gap theorem for self-shrinkers in arbitrary codimension.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/20afbb16138c4070ceae4788d07d374e5e1feaab
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Complete self-shrinkers of the mean curvature flow (2012, methodology): “In [5, 10, 15, 16] and so on, they assume that M has polynomial volume growth.”
- The rigidity theorems of self-shrinkers (2011, unknown): “The first gap of the squared norm of the second fundamental form for selfshrinkers was obtained by Cao-Li [2] (which generalized the codimension 1 case in [15]).”
- Mean Curvature Flow Solitons in the Presence of Conformal Vector Fields (2017, background): “5 extends to our much more general setting results proved by Cao and Li [8] and Ding and Xin [19] for self-shrinkers in the Euclidean space.”