Some results on Chern's problem

Details Some results on Chern's problem Some results on Chern's problem

2010-12-06

arxiv.org/abs/1012.1073v1

Mathematics

Differential Geometry

Scientific paper

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 $\de(n)$ depending only on $n,$ such that if $n\leq S\leq n
+\delta(n)$, then $S\equiv n$, i.e., $M$ is a Clifford minimal hypersurface, in
particular, when $n\ge 6,$ the pinching constant $\de(n)=\f{n}{23}.$

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