边界类光的常r阶F-平均曲率类空超曲面  

Spacelike Hypersurfaces of Constant rth F-mean Curvature with Light-like Boundary

作　　者：张远征 Yuan Zheng ZHANG(School of Mathematics,Shanghai University of Finances and Economics,Shanghai 200433,P.R.China)

机构地区：[1]上海财经大学数学学院,上海200433

出　　处：《数学学报（中文版）》2023年第2期277-292,共16页Acta Mathematica Sinica：Chinese Series

摘　　要：设W_(F(t))是以(n-1)-维圆球面为类光边界的紧致类空Wullf形,对应的F(t(v))是H^(n)上的满足某凸条件的旋转不变函数.本文利用度量扰动和积分公式的方法,证得L^(n+1)中与W_(F(t))相切于边界且有常r阶F-平均曲率(2≤r≤n)的类空超曲面必为W_(F(t)).Let W_(F(t)),corresponding to a rotation invariant function F(t(v))with a convexity condition on the upper hyperboloid H_(+)_(n),be a compact space-like Wulff shape bounded by a light-like(n-1)-round sphere.By applying perturbation metric and some integral formulae,we show that the only spacelike hypersurface with constant rth F-mean curvature in L^(n+1),which is tangent to W_(F(t))on the boundary,is the Wulff shape.

关 键 词：类空Wulff形 类光边界 r阶F-平均曲率 积分公式 

分 类 号：O186.86[理学—数学]