In this paper a flow of convex hypersurfaces in the Euclidean space by the linear-combination of the mean curvature and the n-th root of the Gauss-Kronecker curvature is considered. It is proved that such deforming co...In this paper a flow of convex hypersurfaces in the Euclidean space by the linear-combination of the mean curvature and the n-th root of the Gauss-Kronecker curvature is considered. It is proved that such deforming convex hypersurfaces converge to a round sphere in the Huisken's sense.展开更多
The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in R^(n).They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several ge...The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in R^(n).They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several geometric properties of such hypersurfaces.In particular,they discover a class of non-compact rotational hypersurfaces with constant and negative Gauss-Kronecker curvature and finite volume,which can be seen as the higher-dimensional generalization of the pseudo-sphere.展开更多
Given a bounded convex domain Ω with C∞ boundary and a function ψ∈C∞（δΩ）, Li-Simon-Chen can construct an Euclidean complete and W-complete convex hypersurface M with constant affine Gauss-Kronecker curvature,...Given a bounded convex domain Ω with C∞ boundary and a function ψ∈C∞（δΩ）, Li-Simon-Chen can construct an Euclidean complete and W-complete convex hypersurface M with constant affine Gauss-Kronecker curvature, and they guess the M is also affine complete. In this paper, we give a confirmation answer.展开更多
In this paper, we consider the infinitesimal I- and Il-isometry deformations of submanifolds immersed in a space form N of constant curvature. We obtain some results which are new even in the case of N being the Eucli...In this paper, we consider the infinitesimal I- and Il-isometry deformations of submanifolds immersed in a space form N of constant curvature. We obtain some results which are new even in the case of N being the Euclidean space. At the same time, we generalize some classical results in E-3 Go the submanifolds immersed in a space form of constant curvature.展开更多
文摘In this paper a flow of convex hypersurfaces in the Euclidean space by the linear-combination of the mean curvature and the n-th root of the Gauss-Kronecker curvature is considered. It is proved that such deforming convex hypersurfaces converge to a round sphere in the Huisken's sense.
基金Peking University for providing financial support for the first author
文摘The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in R^(n).They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several geometric properties of such hypersurfaces.In particular,they discover a class of non-compact rotational hypersurfaces with constant and negative Gauss-Kronecker curvature and finite volume,which can be seen as the higher-dimensional generalization of the pseudo-sphere.
基金Supported by National Natural Science Foundation (No. 10771146)RFDP
文摘Given a bounded convex domain Ω with C∞ boundary and a function ψ∈C∞（δΩ）, Li-Simon-Chen can construct an Euclidean complete and W-complete convex hypersurface M with constant affine Gauss-Kronecker curvature, and they guess the M is also affine complete. In this paper, we give a confirmation answer.
文摘In this paper, we consider the infinitesimal I- and Il-isometry deformations of submanifolds immersed in a space form N of constant curvature. We obtain some results which are new even in the case of N being the Euclidean space. At the same time, we generalize some classical results in E-3 Go the submanifolds immersed in a space form of constant curvature.
