Pogorelov Type Estimates For A Class Of Fully Nonlinear Elliptic Equations

Pogorelov type estimation plays a crucial role in the study of Bernstein’s theorem or rigidity theorem for completely nonlinear elliptic equations,and has attracted the attention of many scholars.Currently about Hessian type equations Pogorelov type estimation has been abundantly successful,while Pogorelov estimation results on Hessian quotient equations have yet to be explored.This paper examines a special class of Hessian quotient equations derived from related problems in conformal and complex geometry,and discusses Pogorelov type estimation of this equation.The main body of this thesis is organized as follows.In Chapter 1,The background and significance of the Pogorelov type estimation of the Hessian quotient equation are introduced,as well as the main conclusions of this dissertation.In Chapter 2,The basic concepts,lemma and symbolic descriptions of Hessian operators are given.In Chapter3,The process of proving the theorem is given in detail.