Asymptotic Estimation and Existence of A Coupled System Model Based on Symmetric Space of Riemannian Manifold

2017 3rd International Conference on Environmental Science and Material Application

生态环境科学;材料科学

Deng, Shuxian^1 ; Li, Hongen^1

Department of Basic Courses, Zhengzhou University of Industrial Technology, Zhengzhou

451150, China^1

关键词: Analytic properties;    Asymptotic estimation;    Classification theory;    Elliptic and parabolic equations;    Euclidean Geometry;    Hyperbolic polynomials;    Riemannian manifold;    Symmetric functions;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/108/2/022026/pdf
DOI  :  10.1088/1755-1315/108/2/022026

来源: IOP

【 摘 要 】

In this paper, we will discuss the fully nonlinear elliptic and parabolic equations related to classical Euclidean geometry and conformal geometry. Some algebraic and analytic properties of concave symmetric functions and Garding's theory of hyperbolic polynomials are collected in the appendix. According to the classification theory of Riemann symmetry space, we use transformation to convert the subalgebra of a very tight part to a very noncompact subalgebra. By calculating the projection, we calculate the section curvature of all irreducible Riemann symmetric spaces. Using the classification theory of the maximal subfamily of abstract roots and the control chart, we calculate the partial positive partial negative values of the curvature of all irreducible Riemann symmetric spaces.