On Chernʼs problem for rigidity of minimal hypersurfaces in the spheres

By Qi Ding, Y. Xin. 2011

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Abstract For a compact minimal hypersurface M in S n + 1 with the squared length of the second fundamental form S we confirm that there exists a positive constant δ ( n ) depending only on n , such that if n ⩽ S ⩽ n + δ ( n ) , then S ≡ n , i.e., M is a Clifford minimal hypersurface, in particular, when n ⩾ 6 , the pinching constant δ ( n ) = n 23 .

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d159e50e120dcee1b5607665e320aadcbed49692