A remark on compact hypersurfaces with constant mean curvature in space forms
A remark on compact hypersurfaces with constant mean curvature in space forms
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DOI：
10.1016/j.bulsci.2016.04.002
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发表时间：
2014-10
期刊：
影响因子：
--
通讯作者：
G. Catino
中科院分区：
文献类型：
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作者：
G. Catino
本文刻划了n≥ 2维常平均曲率H的紧致超曲面浸入常曲率空间形式中，并满足一个最优积分pinching条件：它们或者是全脐的，或者当n≥ 3且H <$0时，它们局部包含在一个旋转超曲面中.在二维情形下，积分拼挤条件简化为一个拓扑假设，从而恢复了经典的Hopf-Chern结果.
In this note we characterize compact hypersurfaces of dimension n≥ 2 with constant mean curvature H immersed in space forms of constant curvature and satisfying an optimal integral pinching condition: they are either totally umbilical or, when n≥ 3 and H≠ 0, they are locally contained in a rotational hypersurface. In dimension two, the integral pinching condition reduces to a topological assumption and we recover the classical Hopf–Chern result.