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Liouville—Ttype Theorems for Conformal gaussian curvature Equations in R^2

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Acta Mathematica Sinica,English Series 2003年第1期19卷 63-68页

作者： YunYanYANG LMAM SchoolofMathematicalSciencesPekingUniversityBeijing100871

In this paper, we derive an elementary identity for smooth solutions of the following equation:$$\Delta u\left( x \right) + K\left( x \right)e^{2u\left( x \right)} = 0\,{\rm in}\,R^2 $$and use it to get some global pr... 详细信息

关键词： gaussian curvature Total curvature Obata type identity

An Isometric Embedding of Mbius Band with Positive gaussian curvature

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Acta Mathematica Sinica,English Series 2004年第6期20卷 961-964页

作者： Hui Xia HE Zi Zhou TANG Department of Mathematical Sciences Tsinghua University College of Mathematical Sciences Beijing Normal University

The main purpose of this paper is to show that there is an isometric embedding from M?bius band to ?4 with positive gaussian curvature.

关键词： Veronese map gaussian curvature Isometric immersion

The Concavity of the gaussian curvature of the Convex Level Sets of p-Harmonic Functions with Respect to the Height

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Communications in Mathematics and Statistics 2013年第4期1卷 465-489页

作者： Xi-Nan Ma Wei Zhang School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026AnhuiChina School of Mathematics&Statistics Lanzhou UniversityLanzhou 730000GansuChina

For the p-harmonic function with strictly convex level sets,we find an auxiliary function which comes from the combination of the norm of gradient of the p-harmonic function and the gaussian curvature of the level sets of p-harmonic function.We prove that this curvature function is concave with respect to the height of the p-harmonic function.This auxiliary function is an affine function of the height when the p-harmonic function is the p-Green function on ball.

关键词： p-harmonic function Level set gaussian curvature Support function Maximum prinicple

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紧黎曼曲面上锥度量的高斯博内公式

Chinese Quarterly Journal of Mathematics 2024年第2期39卷 180-184页

作者：方晗兵许斌杨百瑞 Mathematics Department Stony Brook UniversityNY 11794United States CAS Wu Wen-Tsun Key Laboratory of Mathematics and School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026China School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026China

We prove a generalization of the classical Gauss-Bonnet formula for a conical metric on a compact Riemann surface provided that the gaussian curvature is Lebesgue integrable with respect to the area form of the metric... 详细信息

关键词： Gauss-Bonnet formula Conical metric Riemann surface gaussian curvature Lebesgue integrable

Singularity radius gradient-based rapid singularity-escape steering law for SGCMGs

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Chinese Journal of Aeronautics 2020年第10期33卷 2728-2742页

作者： Tao YI Yunhai GENG Baolin WU Research Center of Satellite Technology Harbin Institute of TechnologyHarbin 150080China

In order to visualize singularity of SGCMGs in gimbal angle space,a novel continuous bounded singularity parameter--Singularity Radius,whose sign can distinctly determine singularity type,is proposed.Then a rapid singularity-escape steering law is proposed basing on gradient of Singularity Radius and residual base vector to drive the SGCMG system to neighboring singular boundary,and quickly escape elliptic singularities.Finally,simulation results on Pyramid-type and skew-type configuration demonstrate the effectiveness and rapidness of the proposed steering law.

关键词： gaussian curvature Rapid singularity escape Single gimbal control moment gyroscope Singularity-escape steering law Singularity parameter Singularity type

On Pseudo-Holomorphic Curves from Two-Spheres into a Complex Grassmannian G(2, 5)

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Acta Mathematica Sinica,English Series 2010年第4期26卷 759-762页

作者： Xiao Xiang JIAO Department of Mathematics Graduate University of Chinese Academy of Sciences Beijing 100049 P. R. China

Let s ： S2 → G（2, 5） be a linearly full totally unramified pseudo-holomorphic curve with constant gaussian curvature K in a complex Grassmann manifold G（2, 5）. It is prove that K is either 1 4 1 or 4/5 if s is non-±holomorphic. Furthermore, K = 1/3 if and only if s is totally real. We also prove that the gaussian curvature K is either 1 or -4/3 if s is a non-degenerate holomorphic curve under some conditions.

关键词： pseudo-holomorphic curves gaussian curvature harmonic seouence. Kaihler angle

CONFORMAL DEFORMATION OF COMPLETE SURFACE WITH NEGATIVE curvature

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Chinese Annals of Mathematics,Series B 1997年第2期18卷 173-180页

作者： ZHOU DETANG Department of Mathematics Shandong UniversityJinanShandong 250100China.

The author considers the problem of deforming the metric on a complete negatively curved surface conformal to another metric whose Gauss curvature is nonpositive.

关键词： Riemannian manifold Conformal deformation gaussian curvature

From the second gradient operator and second class of integral theorems to gaussian or spherical mapping invariants

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Applied Mathematics and Mechanics(English Edition) 2008年第7期29卷 855-862页

作者：殷雅俊吴继业黄克智范钦珊 Department of Engineering Mechanics School of AerospaceTsinghua University Division of Mechanics Nanjing University of TechnologyNanjing 211816P.R.China Division of Mechanics Nanjing University of Technology

By combining of the second gradient operator, the second class of integral theorems, the gaussian-curvature-based integral theorems and the gaussian （or spherical） mapping, a series of invariants or geometric conservation quantities under gaussian （or spherical） mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed

关键词： the second gradient operator integral theorem gaussian curvature gaussian （or spherical） mapping mapping invariant

CONSTRUCTION OF HOMOGENEOUS MINIMAL 2-SPHERES IN COMPLEX GRASSMANNIANS

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Acta Mathematica Scientia 2011年第5期31卷 1889-1898页

作者：费杰焦晓祥许小卫 Department of Mathematics Graduate University of Chinese Academy of Sciences Department of Mathematics University of Science and Technology of China

In this paper, we construct a class of homogeneous minimal 2-spheres in complex Grassmann manifolds by applying the irreducible unitary representations of SU （2）. Furthermore, we compute induced metrics, gaussian curvatures, Khler angles and the square lengths of the second fundamental forms of these homogeneous minimal 2-spheres in G（2, n ＋ 1） by making use of Veronese sequence.

关键词： homogeneous 2-sphere gaussian curvature Khler angle Veronese sequence complex Grassmann manifold