欧氏空间中常高阶平均曲率紧致凸超曲面与高斯映像
On the Gauss image of compact and convex hypersurfaces with a constant higher order mean curvature in Euclidean space

针对（n+1）维欧氏空间Rn+1中紧致无边凸超曲面M，利用一个已知的积分公式，并提出一种新的技巧，证明了：如果存在一个整数r（1≤r≤n－1） 使得M的第r阶高阶平均曲率Hr是常数，并且M的高斯映照是到标准单位球面Sn的拓扑同胚，则M全脐.
For an oriented，compact and convex hypersurface M without boundary in the （n+1）dimensional Euclidean space Rn+1，we apply a known integral formula and put out a new skill to prove that if there exits an integer r （1≤r≤n－1） such that the r-mean curvature Hr is a constant and if the Gauss map of M is a topological homeomorphism onto the standard unit sphere Sn，then M is totally umbilical