A rigidity theorem on the second fundamental form for self-shrinkers

Abstract

In Theorem 3.1 of [12], we proved a rigidity result for self-shrinkers under the integral condition on the norm of the second fundamental form. In this paper, we relax the such bound to any finite constant (see Theorem 4.4 for details).

17 pages

References in corpus (4)

• On the self-shrinking systems in arbitrary codimension spaces
• On the rigidity of mean convex self-shrinkers
• A maximum principle for self-shrinkers and some consequences
• New result on Chern conjecture for minimal hypersurfaces and its application