A Class Of Gauss Curvature Flows And Its Application To An Even Dual Orlicz-minkowski Type Problem

Curvature flow is an important research field in geometric analysis.It is often used in the study of several Minkowski type problems in convex geometry,so it has attracted extensive attention.In this paper,we consider a class of anisotropic Gauss curvature flows and obtain the long-time existence.As an application,an existence result of the even solution has been obtained for a class of Monge–Ampère type equations,which associated a dual Orlicz–Minkowski type problem for the even measure.This paper is mainly divided into the following four parts:The first part introduces the research background and current situation of curvature flow problem and gives the main theorems obtained in this paper.The second part gives some necessary preliminary knowledge,including the relevant definition of hypersurface,the proof of lemma,and prepares for the following research.The third part gives the proof of the required lemma and establishes a priori estimate.In the fourth part,based on a priori estimate,we obtain the long time existence of solutions for a class of anisotropic Gaussian curvature flow by using the uniform parabolic equation theory,and further obtain the existence of even solutions for a class of Monge-Amp(?)re type equations derived from the dual Orlicz Minkowski type problems.