<正> The notion of super-isometric dilation is introduced and some elementary properties of this dilation are established. It is shown that the Bergman shift is super-isometrically dilatable, and it is proved, i...<正> The notion of super-isometric dilation is introduced and some elementary properties of this dilation are established. It is shown that the Bergman shift is super-isometrically dilatable, and it is proved, in addition, that for φ,ψ and f in H~∞(D), is unitarily equivalent to M_f iff φ=ψ=f=const. provided some finite condition is satisfied.展开更多
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
基金Project supported by the National Natural Science Foundation of China.
文摘<正> The notion of super-isometric dilation is introduced and some elementary properties of this dilation are established. It is shown that the Bergman shift is super-isometrically dilatable, and it is proved, in addition, that for φ,ψ and f in H~∞(D), is unitarily equivalent to M_f iff φ=ψ=f=const. provided some finite condition is satisfied.
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.
