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math.DG2010
The second pinching theorem for hypersurfaces with constant mean curvature in a sphere
Hong-Wei Xu, Zhi-Yuan Xu
We generalize the second pinching theorem for minimal hypersurfaces in a sphere due to Peng-Terng, Wei-Xu, Zhang, and Ding-Xin to the case of hypersurfaces with small constant mean…
math.DG2010★ 2 cited
An Optimal Differentiable Sphere Theorem for Complete Manifolds
Hong-Wei Xu, Juan-Ru Gu
A new differentiable sphere theorem is obtained from the view of submanifold geometry. An important scalar is defined by the scalar curvature and the mean curvature of an oriented…