Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximatin...Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformal mappings in the plane is discussed.展开更多
This paper gets the Beltrami equations satisfied by a 1-quasiconformal mapping, which are exactly CR or anti-CR equations on （2,2）-type quadric Q0. This means a 1-quasiconformal mapping on Q0 is CR or anti-CR. This ...This paper gets the Beltrami equations satisfied by a 1-quasiconformal mapping, which are exactly CR or anti-CR equations on （2,2）-type quadric Q0. This means a 1-quasiconformal mapping on Q0 is CR or anti-CR. This reduces the determination of 1- quasiconformal mappings to a problem on the theory of several complex analysis. The result about the group of CR automorphisms is used to determine the unit component of group of 1-quasiconformal mappings.展开更多
In this paper, we consider and resolve a geometric problem by using μ（z）-homeomorphic theory, which is the generalization of quasiconformal mappings. A sufficient condition is given such that a Ct-two-real-dimensio...In this paper, we consider and resolve a geometric problem by using μ（z）-homeomorphic theory, which is the generalization of quasiconformal mappings. A sufficient condition is given such that a Ct-two-real-dimensional connected orientable manifold with almost positive definite metric can be made into a Riemann surface by the method of isothermal coordinates. The result obtained here is actually a generalization of Chern＇s work in 1955.展开更多
This paper is devoted to the inverse design of strained graphene surfaces for the control of electrons in the semi-classical optical-like regime.Assuming that charge carriers are described by the Dirac equation in cur...This paper is devoted to the inverse design of strained graphene surfaces for the control of electrons in the semi-classical optical-like regime.Assuming that charge carriers are described by the Dirac equation in curved-space and exploiting the fact that wave propagation can be described by ray-optics in this regime,a general computational strategy is proposed in order to find strain fields associated with a desired effective refractive index profile.The latter is first determined by solving semi-classical trajectories and by optimizing a chosen objective functional using a genetic algorithm.Then,the graded refractive index corresponding to the strain field is obtained by using its connection to the metric component in isothermal coordinates.These coordinates are evaluated via numerical quasiconformal transformations by solving the Beltrami equation with a finite volume method.The graphene surface deformation is finally optimized,also using a genetic algorithm,to reproduce the desired index of refraction.Some analytical results and numerical experiments are performed to illustrate the methodology.展开更多
We show that conformal mappings between the Engel groups are CR or anti-CR mappings. This reduces the determination of conformal mappings to a problem in the theory of several complex analysis.The result about the gro...We show that conformal mappings between the Engel groups are CR or anti-CR mappings. This reduces the determination of conformal mappings to a problem in the theory of several complex analysis.The result about the group of CR automorphisms is used to determine the identity component of the group of conformal mappings on the Engel group.展开更多
基金This project is supported in part by NSF of China(60575004, 10231040)NSF of GuangDong, Grants from the Ministry of Education of China(NCET-04-0791)Grants from Sun Yat-Sen University
文摘Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformal mappings in the plane is discussed.
基金Supported by the National Natural Science Foundation of China (10571155)
文摘This paper gets the Beltrami equations satisfied by a 1-quasiconformal mapping, which are exactly CR or anti-CR equations on （2,2）-type quadric Q0. This means a 1-quasiconformal mapping on Q0 is CR or anti-CR. This reduces the determination of 1- quasiconformal mappings to a problem on the theory of several complex analysis. The result about the group of CR automorphisms is used to determine the unit component of group of 1-quasiconformal mappings.
基金Project (No. 10101023) supported by the National Natural Science Foundation of China
文摘In this paper, we consider and resolve a geometric problem by using μ（z）-homeomorphic theory, which is the generalization of quasiconformal mappings. A sufficient condition is given such that a Ct-two-real-dimensional connected orientable manifold with almost positive definite metric can be made into a Riemann surface by the method of isothermal coordinates. The result obtained here is actually a generalization of Chern＇s work in 1955.
文摘This paper is devoted to the inverse design of strained graphene surfaces for the control of electrons in the semi-classical optical-like regime.Assuming that charge carriers are described by the Dirac equation in curved-space and exploiting the fact that wave propagation can be described by ray-optics in this regime,a general computational strategy is proposed in order to find strain fields associated with a desired effective refractive index profile.The latter is first determined by solving semi-classical trajectories and by optimizing a chosen objective functional using a genetic algorithm.Then,the graded refractive index corresponding to the strain field is obtained by using its connection to the metric component in isothermal coordinates.These coordinates are evaluated via numerical quasiconformal transformations by solving the Beltrami equation with a finite volume method.The graphene surface deformation is finally optimized,also using a genetic algorithm,to reproduce the desired index of refraction.Some analytical results and numerical experiments are performed to illustrate the methodology.
基金supported by National Natural Science Foundation of China(Grant No.10871172)
文摘We show that conformal mappings between the Engel groups are CR or anti-CR mappings. This reduces the determination of conformal mappings to a problem in the theory of several complex analysis.The result about the group of CR automorphisms is used to determine the identity component of the group of conformal mappings on the Engel group.
