Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. ...Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.展开更多
Let M be a concircularly fiat totally real minimal submanifold in CP4. The infimum Vm of the volume V （M） of M is obtained, also the necessary and sufficient conditions of ＂V（M）=Vm＂ is given.
Interference alignment(IA) is one of the promising measures for the multi-user network to manage interference. The rank constraints rank minimization means that interference spans the lowest dimensional subspace and t...Interference alignment(IA) is one of the promising measures for the multi-user network to manage interference. The rank constraints rank minimization means that interference spans the lowest dimensional subspace and the useful signal spans all available spatial dimensions. In order to improve the performance of two-way relay network, we can use rank constrained rank minimization(RCRM) to solve the IA problem. This paper proposes left reweighted nuclear norm minimization-γalgorithm and selective coupling reweighted nuclear norm minimization algorithm to implement interference alignment in two-way relay networks. The left reweighted nuclear norm minimization-γ algorithm is based on reweighted nuclear norm minimization algorithm and has a novel γ choosing rule. The selective coupling reweighted nuclear norm minimization algorithm weighting methods choose according to singular value of interference matrixes. Simulation results show that the proposed algorithms considerably improve the sum rate performance and achieve the higher average achievable multiplexing gain in two-way relay interference networks.展开更多
In this paper,the minimal conjecture on the Veronese Generating submanifolds in S(1)5 is generalized to minmal submanifolds in Sm. Two classes of the Generating submanifolds of spherical minimal submanifolds in Minkow...In this paper,the minimal conjecture on the Veronese Generating submanifolds in S(1)5 is generalized to minmal submanifolds in Sm. Two classes of the Generating submanifolds of spherical minimal submanifolds in Minkowski space are respectively space-like Minimal submanifolds of Hyperbolic space and pseudo-Rie-mannian Minimal submanifolds of pseudo-Riemannian sphere and they are of 1-type submanifolds in Minkowski space is proved.展开更多
The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type...The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type Chen submanifolds,mass-symmetrie hypersurfaces and Dupin hypersurfaces in E_3~m are obtained. The classification theorems of 3-type hypersurfaces and null 2-type curves in E_3~m are also proved.展开更多
We obtain new complete minimal surfaces in the hyperbolic space H3, by using Ribaucour transformations. Starting with the family of spherical catenoids in H^3 found by Mori(1981), we obtain 2-and 3-parameter families ...We obtain new complete minimal surfaces in the hyperbolic space H3, by using Ribaucour transformations. Starting with the family of spherical catenoids in H^3 found by Mori(1981), we obtain 2-and 3-parameter families of new minimal surfaces in the hyperbolic space, by solving a non trivial integro-differential system. Special choices of the parameters provide minimal surfaces whose parametrizations are defined on connected regions of R^2 minus a disjoint union of Jordan curves. Any connected region bounded by such a Jordan curve, generates a complete minimal surface, whose boundary at infinity of H^3 is a closed curve. The geometric properties of the surfaces regarding the ends, completeness and symmetries are discussed.展开更多
The author studies minimal surfaces in 3-dimensional solvable Lie groups with left invariantRiemannian metrics. A Weierstraβ type integral representation formula for minimal surfaces isobtained.
文摘Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.
基金Supported by the NSF of Education Department of Henan Province(20021100002)Supported by the NSF of Education Department of Henan Province(200510475038)
文摘Let M be a concircularly fiat totally real minimal submanifold in CP4. The infimum Vm of the volume V （M） of M is obtained, also the necessary and sufficient conditions of ＂V（M）=Vm＂ is given.
基金supported by the National Science Foundation of China (NO.61271240, 61671253)
文摘Interference alignment(IA) is one of the promising measures for the multi-user network to manage interference. The rank constraints rank minimization means that interference spans the lowest dimensional subspace and the useful signal spans all available spatial dimensions. In order to improve the performance of two-way relay network, we can use rank constrained rank minimization(RCRM) to solve the IA problem. This paper proposes left reweighted nuclear norm minimization-γalgorithm and selective coupling reweighted nuclear norm minimization algorithm to implement interference alignment in two-way relay networks. The left reweighted nuclear norm minimization-γ algorithm is based on reweighted nuclear norm minimization algorithm and has a novel γ choosing rule. The selective coupling reweighted nuclear norm minimization algorithm weighting methods choose according to singular value of interference matrixes. Simulation results show that the proposed algorithms considerably improve the sum rate performance and achieve the higher average achievable multiplexing gain in two-way relay interference networks.
文摘In this paper,the minimal conjecture on the Veronese Generating submanifolds in S(1)5 is generalized to minmal submanifolds in Sm. Two classes of the Generating submanifolds of spherical minimal submanifolds in Minkowski space are respectively space-like Minimal submanifolds of Hyperbolic space and pseudo-Rie-mannian Minimal submanifolds of pseudo-Riemannian sphere and they are of 1-type submanifolds in Minkowski space is proved.
基金Supported by the National Fundations of Natural sciences. Supported by the Henan Fundations of Scientific Committee.
文摘The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type Chen submanifolds,mass-symmetrie hypersurfaces and Dupin hypersurfaces in E_3~m are obtained. The classification theorems of 3-type hypersurfaces and null 2-type curves in E_3~m are also proved.
基金supported by a Post-Doctoral Fellowship offered by CNPqpartially supported by CNPq, Ministry of Science and Technology, Brazil (Grant No. 312462/2014-0)
文摘We obtain new complete minimal surfaces in the hyperbolic space H3, by using Ribaucour transformations. Starting with the family of spherical catenoids in H^3 found by Mori(1981), we obtain 2-and 3-parameter families of new minimal surfaces in the hyperbolic space, by solving a non trivial integro-differential system. Special choices of the parameters provide minimal surfaces whose parametrizations are defined on connected regions of R^2 minus a disjoint union of Jordan curves. Any connected region bounded by such a Jordan curve, generates a complete minimal surface, whose boundary at infinity of H^3 is a closed curve. The geometric properties of the surfaces regarding the ends, completeness and symmetries are discussed.
基金Partially supported by Grant-in-Aid for Encouragement of Young Scientists (No. 12740051), Japan Society for Promotion of Science.
文摘The author studies minimal surfaces in 3-dimensional solvable Lie groups with left invariantRiemannian metrics. A Weierstraβ type integral representation formula for minimal surfaces isobtained.
