A GAP THEOREM OF SELF-SHRINKERS

By Qing Cheng, G. Wei. 2012

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In this paper, we study complete self-shrinkers in Euclidean space and prove that an n-dimensional complete self-shrinker with polynomial volume growth in Euclidean space R n+1 is isometric to either R n , S n ( √ n), or R n m × S m ( √ m), 1 ≤ m ≤ n−1, if the squared norm S of the second fundamental form is constant and satisfies S < 10 7 .

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/01a261becaf06161e059e79d700c572fc72f21f6