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Electronic Structure and Electron-transport Properties of Peanut-shaped C_(60) Polymers with a Negative gauss curvature

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复旦学报（自然科学版） 2007年第5期46卷 632-633页

作者： J.Onoe Y.Ochiai T.Ito S.Kimura S.Ueda Y.Noguchi S.Ishii K.Ohno Y.Toda Research Laboratory for Nuclear Reactors Tokyo Institute of Technology Department of Materials Technology Chiba University UVSOR Institute for Molecular Science Department of Physics Yokohama National University Department of Applied Physics Hokkaido University

1 Results When a C60 film was irradiated with electron-beam (EB) with an incident energy of 3 kV, a peanut-shaped C60 polymer with metallic properties was formed[1], as shown in Fig.1. To elucidate the origin of the metallic properties of the peanut-shaped polymer, we examined the valence photoelectron spectra of the polymer using in situ high-resolution photoelectron spectroscopy and found that the electronic states of the polymer came across the Fermi level (EF)[2]. Interestingly, the spectral shape i...

关键词： electron-transport C60 polymers gauss curvature

ON HOLOMORPHIC CURVES OF CONSTANT curvature IN THE COMPLEX GRASSMANN MANIFOLD G(2,5)

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Acta Mathematica Scientia 2011年第1期31卷 237-248页

作者：焦晓祥彭家贵 Department of Mathematics Graduate University Chinese Academy of Sciences

In this article, it is proved that there doesn’t exist any nonsingular holomorphic sphere in complex Grassmann manifold G（2, 5） with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if φ ： S2 ... 详细信息

关键词： gauss curvature holomorphic curve complex Grassmann manifold

Minimal two-spheres with constant curvature in the quaternionic projective space

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Science China Mathematics 2020年第5期63卷 993-1006页

作者： Jie Fei Chiakuei Peng Xiaowei Xu Department of Mathematical Sciences Xi’an Jiaotong-Liverpool UniversitySuzhou 215123China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Department of Mathematics University of Science and Technology of ChinaHefei 230026China Wu Wen-Tsun Key Laboratory of Mathematics University of Science and Technology of ChinaChinese Academy of SciencesHefei 230026China

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-spheres in HPnare obtained than what Ohnita conjectured in the paper"Homogeneous harmonic maps into complex projective spaces.Tokyo J Math,1990,13:87–116".

关键词： minimal two-sphere gauss curvature quaternionic projective space

Generalized Solution of a Kind of Nonparametric curvature Evolution with Boundary Condition

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Acta Mathematica Sinica,English Series 2006年第2期22卷 455-468页

作者： Li CHEN Hui Zhao LIU Department of Mathematical Science Tsinghua University Department of Applied Mathematics Hebei University of Technology

The existence and uniqueness of the generalized solution for a kind of nonparametric curvature flow problem are obtained. This kind of curvature flow problem describes the evolution of graphs with speed depending on t... 详细信息

关键词： gauss curvature First initial-boundary problem Generalized solution Convex-monotone function

Retrieving Topological Information of Implicitly Represented Diffuse Interfaces with Adaptive Finite Element Discretization

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Communications in Computational Physics 2013年第5期13卷 1209-1226页

作者： Jian Zhang Qiang Du Supercomputing center Chinese Academy of SciencesBeijingP.R.China Department of Mathematics Pennsylvania State UniversityUniversity ParkPA 16802USA State Key Laboratory of Space Weather Chinese Academy of SciencesBeijingP.R.China

We consider the finite element based computation of topological quantities of implicitly represented surfaces within a diffuse interface framework.Utilizing an adaptive finite element implementation with effective gradient recovery techniques,we discuss how the Euler number can be accurately computed directly from the numerically solved phase field functions or order parameters.Numerical examples and applications to the topological analysis of point clouds are also presented.

关键词： Diffuse interface model phase field method Euler number gauss curvature adaptive finite element gradient recovery

Totally Real Surfaces of the Cayley Projective Plane with Parallel Mean curvature Vector

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Northeastern Mathematical Journal 2003年第2期19卷 169-173页

作者：苏伟宏 Department of Applied Mathematics Beijing Institute of Technology Beijing100081

It has been shown, under certain conditions on the gauss curvature, every totally real surface of the Cayley projective plane with parallel mean curvature vector is either flat or totally geodesic.

关键词： totally real surface Cayley projective plane gauss curvature

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曲面上的曲率在理论物理中的一些应用

Chinese Quarterly Journal of Mathematics 2023年第3期38卷 221-253页

作者： YANG Yi-song Courant Institute of Mathematical Sciences New York UniversityNY 10012USA

In this survey article,we present two applications of surface curvatures in theoretical physics.The first application arises from biophysics in the study of the shape of cell vesicles involving the minimization of a mean curvature type energy called the Helfrich bending energy.In this formalism,the equilibrium shape of a cell vesicle may present itself in a rich variety of geometric and topological characteristics.We first show that there is an obstruction,arising from the spontaneous curvature,to the existence of a minimizer of the Helfrich energy over the set of embedded ring tori.We then propose a scale-invariant anisotropic bending energy,which extends the Canham energy,and show that it possesses a unique toroidal energy minimizer,up to rescaling,in all parameter regime.Furthermore,we establish some genus-dependent topological lower and upper bounds,which are known to be lacking with the Helfrich energy,for the proposed energy.We also present the shape equation in our context,which extends the Helfrich shape equation.The second application arises from astrophysics in the search for a mechanism for matter accretion in the early universe in the context of cosmic strings.In this formalism,gravitation may simply be stored over a two-surface so that the Einstein tensor is given in terms of the gauss curvature of the surface which relates itself directly to the Hamiltonian energy density of the matter sector.This setting provides a lucid exhibition of the interplay of the underlying geometry,matter energy,and topological characterization of the system.In both areas of applications,we encounter highly challenging nonlinear partial differential equation problems.We demonstrate that studies on these equations help us to gain understanding of the theoretical physics problems considered.

关键词： Mean curvature gauss curvature Bending energy Cell vesicles Topological bounds Shape equations Einstein tensor Cosmic strings Harmonic map model Nirenberg’s problem Conical singularities Deficit angle Conformal metric

Minimal Surfaces in a Unit Sphere

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Journal of Mathematical Research with Applications 2012年第3期32卷 346-354页

作者： Zhonghua HOU,Dan YANG School of Mathematical Science,Dalian University of Technology,Liaoning 116024,P.R.China School of Mathematical Science Dalian University of Technology Liaoning 116024

Let M be a closed surface with positive gauss curvature minimally immersed in a standard Euclidean unit sphere S;.In this paper,we choose a local orthonormal frame field on M,under which the shape operators have very ... 详细信息

关键词： minimal surface gauss curvature normal scalar curvature.