圆球面为边的常F-平均曲率类空超曲面

Constant F-Mean Curvature Spacelike Hypersurfaces with Round Boundary

设F(t)是上伪球面H_+~n上时轴旋转不变且满足凸条件的光滑函数.本文证得:Lorentz空间L^(n+1)中,以圆球面S^(n-1)(R)为边界且有非零常F-平均曲率的紧致类空超曲面必为Wulff帽.

Given a rotation invariant function F on the upper hyperboloid Hn＋ which satisfies a convexity condition, we show that the only compact spacelike hypersurfaces in Ln＋1, which have spherical boundary and nonzero constant F-mean curvature, are the Wulff caps.