Let M be a compact minimal hypersurface of sphere Sn+1(1). Let M be H(r)-torus of sphere Sn+1(1).Assume they have the same constant mean curvature H, the result in [1] is that if Spec0 (M, g) =Spec0(M, g),then for 3 ...Let M be a compact minimal hypersurface of sphere Sn+1(1). Let M be H(r)-torus of sphere Sn+1(1).Assume they have the same constant mean curvature H, the result in [1] is that if Spec0 (M, g) =Spec0(M, g),then for 3 ≤ n ≤ 6,r2 ≤n-1/n or n > 6,r2 ≥ n-1/n, then M is isometric to M. We improvedthe result and prove that: if Spec0(M, g) =Spec0(M, g), then M is isometric to M. Generally, if Specp(M,g) =Specp(M, g), here p is fixed and satisfies that n(n - 1) ≠ 6p(n - p), then M is isometric to M.展开更多
The authors establish some uniform estimates for the distance to halfway points of minimalgeodesics in terms of the distantce to end points on some types of Riemannian manifolds, andthen prove some theorems about the ...The authors establish some uniform estimates for the distance to halfway points of minimalgeodesics in terms of the distantce to end points on some types of Riemannian manifolds, andthen prove some theorems about the finite generation of fundamental group of Riemannianmanifold with nonnegative Ricci curvature, which support the famous Milnor conjecture.展开更多
基金Supported by National Natural Science Foundation of China (10371047)
文摘Let M be a compact minimal hypersurface of sphere Sn+1(1). Let M be H(r)-torus of sphere Sn+1(1).Assume they have the same constant mean curvature H, the result in [1] is that if Spec0 (M, g) =Spec0(M, g),then for 3 ≤ n ≤ 6,r2 ≤n-1/n or n > 6,r2 ≥ n-1/n, then M is isometric to M. We improvedthe result and prove that: if Spec0(M, g) =Spec0(M, g), then M is isometric to M. Generally, if Specp(M,g) =Specp(M, g), here p is fixed and satisfies that n(n - 1) ≠ 6p(n - p), then M is isometric to M.
基金the National Natural Science Foundation of China(No.19971081).
文摘The authors establish some uniform estimates for the distance to halfway points of minimalgeodesics in terms of the distantce to end points on some types of Riemannian manifolds, andthen prove some theorems about the finite generation of fundamental group of Riemannianmanifold with nonnegative Ricci curvature, which support the famous Milnor conjecture.
