S^(n+1)中具有常数曲率的极小超曲面(英文)

MINIMAL HYPER-SURFACES WITH CONSTANT SCALAR CURVATURE IN S n+1

设Ｍｎ是Ｓｎ＋１中紧致极小超曲面。（１）对于较大的自然数ｎ，如果Ｓ＞ｎ，那么Ｓ＝２ｎ；（２）对于较小的自然数ｎ，如果Ｓ＞ｎ那么Ｓ＞５４ｎ。

In this paper we obtain the following theorem:Theorem Let M n be a compact minimal hyper-surfaces in S n+1 (1) . (1) For the larger natural number n , if S>n , then S=2n ; (2) For the smaller natural number n , if S>n , then S>54n .