Complete self-shrinkers of the mean curvature flow

By Qing Cheng, Yejuan Peng. 2012

94 citations recorded by the source corpus.

It is our purpose to study complete self-shrinkers in Euclidean space. By introducing a generalized maximum principle for $$\mathcal {L}$$L-operator, we give estimates on supremum and infimum of the squared norm of the second fundamental form of self-shrinkers without assumption on polynomial volume growth, which is assumed in Cao and Li [5]. Thus, we can obtain the rigidity theorems on complete self-shrinkers without assumption on polynomial volume growth. For complete proper self-shrinkers of dimension 2 and 3, we give a classification of them under assumption of constant squared norm of the second fundamental form.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/72718b2f5162c895b1e5f9accecefea04a92c8a7