Let M be an n（≥ 3）-dimensional completely non-compact spacelike hypersurface in the de Sitter space S1^n＋1 （1） with constant mean curvature and nonnegative sectional curvature. It is proved that M is isometric t...Let M be an n（≥ 3）-dimensional completely non-compact spacelike hypersurface in the de Sitter space S1^n＋1 （1） with constant mean curvature and nonnegative sectional curvature. It is proved that M is isometric to a hyperbolic cylinder or an Euclidean space if H ≥ 1. When 2√n-1/n〈 H 〈 1, there exists a complete rotation hypersurfaces which is not a hyperbolic cylinder.展开更多
In this paper,we prove that the nearly integrable system of the form H(x,y)=h(y)+εP(x,y),x∈T^(n),y∈T^(n),n≥3 admits orbits that pass through any finitely many prescribed small balls on the same energy level H^(-1)...In this paper,we prove that the nearly integrable system of the form H(x,y)=h(y)+εP(x,y),x∈T^(n),y∈T^(n),n≥3 admits orbits that pass through any finitely many prescribed small balls on the same energy level H^(-1)(E)provided that E>min h,if h is convex,andεP is typical.This settles the Arnold diffusion conjecture for convex systems in the smooth category.We also prove the counterpart of Arnold diffusion for the Riemannian metric perturbation of the flat torus.展开更多
基金The NNSFC (10371047) and the NSF (04KJD110192) of the Education Department of Jiangsu Province, China.
文摘Let M be an n（≥ 3）-dimensional completely non-compact spacelike hypersurface in the de Sitter space S1^n＋1 （1） with constant mean curvature and nonnegative sectional curvature. It is proved that M is isometric to a hyperbolic cylinder or an Euclidean space if H ≥ 1. When 2√n-1/n〈 H 〈 1, there exists a complete rotation hypersurfaces which is not a hyperbolic cylinder.
基金supported by National Natural Science Foundation of China (Grant Nos.11790272 and 11631006)supported by National Natural Science Foundation of China (Grant Nos.11790273 and 12271285)。
文摘In this paper,we prove that the nearly integrable system of the form H(x,y)=h(y)+εP(x,y),x∈T^(n),y∈T^(n),n≥3 admits orbits that pass through any finitely many prescribed small balls on the same energy level H^(-1)(E)provided that E>min h,if h is convex,andεP is typical.This settles the Arnold diffusion conjecture for convex systems in the smooth category.We also prove the counterpart of Arnold diffusion for the Riemannian metric perturbation of the flat torus.
