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
We consider the inverse curvature flows of smooth,closed and strictly convex rotation hypersurfaces in space forms M_(κ)^(n+1)with speed function given by F^(-α),whereα∈(0,1]forκ=0,-1,α=1 forκ=1 and F is a smoo...We consider the inverse curvature flows of smooth,closed and strictly convex rotation hypersurfaces in space forms M_(κ)^(n+1)with speed function given by F^(-α),whereα∈(0,1]forκ=0,-1,α=1 forκ=1 and F is a smooth,symmetric,strictly increasing and 1-homogeneous function of the principal curvatures of the evolving hypersurfaces.We show that the curvature pinching ratio of the evolving hypersurface is controlled by its initial value,and prove the long time existence and convergence of the flows.No second derivatives conditions are required on F.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 the National Key R and D Program of China(Grant No.2020YFA0713100)National Natural Science Foundation of China(Grant Nos.11971244 and 11871283)+1 种基金Natural Science Foundation of Tianjin,China(Grant No.19JCQNJC14300)Research(Grant No.KY0010000052)from University of Science and Technology of China。
文摘We consider the inverse curvature flows of smooth,closed and strictly convex rotation hypersurfaces in space forms M_(κ)^(n+1)with speed function given by F^(-α),whereα∈(0,1]forκ=0,-1,α=1 forκ=1 and F is a smooth,symmetric,strictly increasing and 1-homogeneous function of the principal curvatures of the evolving hypersurfaces.We show that the curvature pinching ratio of the evolving hypersurface is controlled by its initial value,and prove the long time existence and convergence of the flows.No second derivatives conditions are required on F.
