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SPHERE: 作品数：621被引量：896H指数：12; 导出分析报告; 相关领域：理学更多>>; 相关作者：佘江峰毛翼飞宋桂娟谈心郭星辰更多>>; 相关机构：南京大学清华大学合肥工业大学中北大学更多>>; 相关期刊：更多>>; 相关基金：国家自然科学基金国家重点基础研究发展计划中国博士后科学基金国家教育部博士点基金更多>>

On the generalized Chern conjecture for hypersurfaces with constant mean curvature in a sphere被引量：2: 《Science China Mathematics》2021年第7期1493-1504,共12页Li Lei Hongwei Xu Zhiyuan Xu; supported by National Natural Science Foundation of China(Grant No.11531012);China Postdoctoral Science Foundation(Grant No.BX20180274);Natural Science Foundation of Zhejiang Province(Grant No.LY20A010024)。; Let M be a compact hypersurface with constant mean curvature in Denote by H and S the mean curvature and the squared norm of the second fundamental form of M,respectively.We verify that there exists a positive constan...; 关键词：generalized Chern conjecture hypersurfaces with constant mean curvature rigidity theorem scalar curvature the second fundamental form

Generic conformally flat hypersurfaces and surfaces in 3-sphere: 《Science China Mathematics》2020年第12期2439-2474,共36页Yoshihiko Suyama; The aim of this paper is to verify that the study of generic conformally flat hypersurfaces in 4-dimensional space forms is reduced to a surface theory in the standard 3-sphere.The conformal structure of generic confo...; 关键词：conformally flat hypersurface system of evolution equations Guichard net integrability condition surface in 3-sphere

Minimal two-spheres with constant curvature in the quaternionic projective space被引量：1: 《Science China Mathematics》2020年第5期993-1006,共14页Jie Fei Chiakuei Peng Xiaowei Xu; supported by National Natural Science Foundation of China(Grant Nos.11471299,11401481 and 11331002)。; In this paper we completely classify the homogeneous two-spheres,especially,the minimal homogeneous ones in the quaternionic projective space HPn.According to our classification,more minimal constant curved two-sphere...; 关键词：minimal two-sphere Gauss curvature quaternionic projective space

A note on semidefinite programming relaxations for polynomial optimization over a single sphere被引量：7: 《Science China Mathematics》2016年第8期1543-1560,共18页HU Jiang JIANG Bo LIU Xin WEN ZaiWen; supported by National Natural Science Foundation of China (Grant Nos. 11401364, 11322109, 11331012, 11471325 and 11461161005);the National High Technology Research and Development Program of China (863 Program) (Grant No. 2013AA122902);the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences;National Basic Research Program of China (973 Program) (Grant No. 2015CB856002); We study two instances of polynomial optimization problem over a single sphere. The first problem is to compute the best rank-1 tensor approximation. We show the equivalence between two recent semidefinite relaxations...; 关键词：polynomial optimization over a single sphere semidefinite programming best rank-1 tensor ap-proximation Bose-Einstein condensates

A note on the entropy of mean curvature flow: 《Science China Mathematics》2015年第12期2611-2620,共10页BAO Chao; The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers and scales, and is invariant under rigid motions and dilations. As a consequence of Huisken's monotonicity formula, en...; 关键词：ENTROPY self-shrinker mean curvature flow SPHERE

On almost complex curves and Hopf hypersurfaces in the nearly Kahler six-sphere: 《Science China Mathematics》2014年第5期1045-1056,共12页HE Ling JIAO XiaoXiang ZHOU XianChao; supported by National Natural Science Foundation of China(Grant No.11071248); We study the almost complex curves and Hopf hypersurfaces in the nearly Khler S6(1),and their relations.For Hopf hypersurfaces,we give a classification theorem under some additional conditions.For compact almost compl...; 关键词：nearly Kahler structure Hopf hypersurface tubular hypersurface almost complex curve

Homological properties of Podle′s quantum spheres: 《Science China Mathematics》2014年第1期69-80,共12页LIU LiYu SHEN YunYi WU QuanShui; supported by National Natural Science Foundation of China (Grant Nos. 10731070 and 11171067);Science and Technology Committee,Shanghai Municipality (Grant No. 11XD1400500);a training program for innovative talents of key disciplines,Fudan University; The standard Podle′s quantum sphere is Artin-Schelter regular as showed by Kra¨hmer(2012).The non-standard Podle′s quantum spheres are proved to be Auslander-regular,Cohen-Macaulay and Artin-Schelter regular in thi...; 关键词：Podle′s QUANTUM sphere Hopf algebra AS-regular Auslander-regular Cohen-Macaulay

CR submanifolds in a sphere and their Gauss maps被引量：1: 《Science China Mathematics》2013年第5期1041-1049,共9页CHENG XiaoLiang JI ShanYu LIU WeiMing; The relationship between CR submanifolds in a sphere and their Gauss maps are investigated.Let V be the image of a sphere by a rational holomorphic map F with degree two in another sphere.It is show that the Gauss map...; 关键词：CR submanifold Gauss maps

Learning rates of regularized regression on the unit sphere被引量：2: 《Science China Mathematics》2013年第4期861-876,共16页CAO FeiLong LIN ShaoBo CHANG XiangYu XU ZongBen; supported by National Natural Science Foundation of China (Grant Nos. 61272023 and 61075054); This paper addresses the learning algorithm on the unit sphere.The main purpose is to present an error analysis for regression generated by regularized least square algorithms with spherical harmonics kernel.The exces...; 关键词：SPHERE regularized regression spherical harmonics kernel rate of convergence

Results on entire solutions for a degenerate critical elliptic equation with anisotropic coefficients被引量：3: 《Science China Mathematics》2011年第2期221-242,共22页CHEN ShaoWei LIN LiShan; supported by National Natural Science Foundation of China (Grant Nos. 10901112, 11001255);Beijing Natural Science Foundation (Grant No. 1102013);China Postdoctoral Science Foundation (Grant No. 20090460548); In this paper, we study the following degenerate critical elliptic equation with anisotropic coefficients-div(|x N | 2α▽u) = K(x)|x N | α·2 * (s)-s |u| 2 * (s)-2 u in R N ,where x = (x 1 , . . . , x N ) ∈ R N , N...; 关键词：weighted Sobolev inequalities Harnack inequality moving sphere method variational identities

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