The second pinching theorem for hypersurfaces with constant mean curvature in a sphere (Q2376877)

The authors prove a main theorem after having reviewed the existing results and fundamental concepts, and introduce their theorem in the context of Chern conjectures and pinching theorems. The proof of the theorem is laborious. As the authors say in the abstract: ``The theorem generalizes 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 curvature.''