有关不能全含于半球中的一些曲面的性质讨论
THE DISCUSSION OF SOME SURFACES WHICH ARE NOT ALL CONTAINED IN A HEMISPHERE

本文主要研究了不能全含于开半球中的一些特殊曲面.利用Lr算子的相关性质,证明了对Sn+1中紧致r-极小超曲面,如果第二基本形式的秩rank (hij)> r,则其不全含在Sn+1的一个开半球中.
In this paper, we mainly study some special surfaces which are not all contained in an open hemisphere. By using properties of Lr operator, we prove that for a compact r-minimal hypersurface in Sn+1, if the rank of the second fundamental form rank(hij) > r then the hypersurface can not be contained in an open hemisphere of Sn+1