紧致超曲面上的谱(英文)

The Spectrum of the Laplace Operation on Compact Hypersurfaces

设 M是 Sn+1 ( 1 )上的紧致极小超曲面 ,M1 ,n- 1 是 S(n+1 ) ( 1 )上的 Clifford极小超曲面 .若它们的谱相同 ,则它们是等距的 .对于 S(n+1 ) ( 1 )上的紧致常平均曲率超曲面和 H ( r) -环 。

Let M be a compact minimal hypersurface of sphere S n+1 (1). Let M 1,n-1  be a Clifford minimal hypersurface of sphere S n+1 (1). If  Spe c°(M)= Spe c°(M 1,n-1 ), then M is isometric to M 1,n-1 . For a compact hypersurface of sphere S n+1 (1) with constant mean curvature and a H torus, under certain conditions isospetrum implies isometric.