The Experts below are selected from a list of 819 Experts worldwide ranked by ideXlab platform

Jie Zhou - One of the best experts on this subject based on the ideXlab platform.

  • Blow-up analysis involving Isothermal Coordinates on the boundary of compact Riemann surface
    arXiv: Differential Geometry, 2020
    Co-Authors: Yunyan Yang, Jie Zhou
    Abstract:

    Using the method of blow-up analysis, we obtain two sharp Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary, as well as the existence of the corresponding extremals. This generalizes early results of Chang-Yang [7] and the first named author [32], and complements Fontana's inequality of two dimensions [15]. The blow-up analysis in the current paper is far more elaborate than that of [32], and particularly clarifies several ambiguous points there. In precise, we prove the existence of Isothermal Coordinate systems near the boundary, the existence and uniform estimates of the Green function with the Neumann boundary condition. Also our analysis can be applied to the Kazdan-Warner problem and the Chern-Simons Higgs problem on compact Riemman surfaces with smooth boundaries.

Zhou Jie - One of the best experts on this subject based on the ideXlab platform.

  • Blow-up analysis involving Isothermal Coordinates on the boundary of compact Riemann surface
    2020
    Co-Authors: Yang Yunyan, Zhou Jie
    Abstract:

    Using the method of blow-up analysis, we obtain two sharp Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary, as well as the existence of the corresponding extremals. This generalizes early results of Chang-Yang [7] and the first named author [32], and complements Fontana's inequality of two dimensions [15]. The blow-up analysis in the current paper is far more elaborate than that of [32], and particularly clarifies several ambiguous points there. In precise, we prove the existence of Isothermal Coordinate systems near the boundary, the existence and uniform estimates of the Green function with the Neumann boundary condition. Also our analysis can be applied to the Kazdan-Warner problem and the Chern-Simons Higgs problem on compact Riemman surfaces with smooth boundaries.Comment: 37 page

Yunyan Yang - One of the best experts on this subject based on the ideXlab platform.

  • Blow-up analysis involving Isothermal Coordinates on the boundary of compact Riemann surface
    arXiv: Differential Geometry, 2020
    Co-Authors: Yunyan Yang, Jie Zhou
    Abstract:

    Using the method of blow-up analysis, we obtain two sharp Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary, as well as the existence of the corresponding extremals. This generalizes early results of Chang-Yang [7] and the first named author [32], and complements Fontana's inequality of two dimensions [15]. The blow-up analysis in the current paper is far more elaborate than that of [32], and particularly clarifies several ambiguous points there. In precise, we prove the existence of Isothermal Coordinate systems near the boundary, the existence and uniform estimates of the Green function with the Neumann boundary condition. Also our analysis can be applied to the Kazdan-Warner problem and the Chern-Simons Higgs problem on compact Riemman surfaces with smooth boundaries.

Yang Yunyan - One of the best experts on this subject based on the ideXlab platform.

  • Blow-up analysis involving Isothermal Coordinates on the boundary of compact Riemann surface
    2020
    Co-Authors: Yang Yunyan, Zhou Jie
    Abstract:

    Using the method of blow-up analysis, we obtain two sharp Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary, as well as the existence of the corresponding extremals. This generalizes early results of Chang-Yang [7] and the first named author [32], and complements Fontana's inequality of two dimensions [15]. The blow-up analysis in the current paper is far more elaborate than that of [32], and particularly clarifies several ambiguous points there. In precise, we prove the existence of Isothermal Coordinate systems near the boundary, the existence and uniform estimates of the Green function with the Neumann boundary condition. Also our analysis can be applied to the Kazdan-Warner problem and the Chern-Simons Higgs problem on compact Riemman surfaces with smooth boundaries.Comment: 37 page

Наталія Миколаївна Аушева - One of the best experts on this subject based on the ideXlab platform.

  • Modeling of Planar Networks Based on the Fractional-rational Curves Isotropic
    Technology audit and production reserves, 2013
    Co-Authors: Наталія Миколаївна Аушева
    Abstract:

    Application of the theory of isotropic curves in the construction of planar networks with specific properties for using in various applied problems is considered in the paper. The main objective is to develop a new method for constructing planar orthogonal and Isothermal Coordinate networks, based on the isotropic fractional-rational n-th order curves. Modeling of isotropic fractional-rational curves, based on the isotropic sides of the characteristic polygons is considered in the paper. The conditions for the position of the reference points are given. It is proved that the weight value does not affect the construction of the isotropic curve. The ratio for the construction of such networks using the conformal mapping is obtained. It is proved that the parametric partial derivatives will satisfy the Cauchy-Riemann equations. The method was developed for further use in surface modeling in three-dimensional space.