Curvature Estimates For Spacelike Graphic Hypersurfaces In Lorentz-Minkowski Space R₁ⁿ⁺¹

The prescribed curvature problems has an important research significance in geometry and partial differential equations,which has attracted the attention of(domestic and foreign)scholars and achieved many important results.In this paper,we can obtain curvature estimates for spacelike admissible graphic hypersurfaces in the(n+1)-dimensional Lorentz-Minkowski space R1n+1,and through which the existence of spacelike admissible graphic hypersurfaces,with prescribed kth Weingarten curvature and Dirichlet boundary data,defined over a strictly convex domain in the hyperbolic space Hn(1)?R1n+1,of center at origin and radius 1,can be proven.The structure of this paper is as follows:In the first chapter,the background of the research on the prescribed curvature problems are introduced,as well as the main conclusions of this dissertation;In the second chapter,the basic knowledge related to this paper,some formulas and symbols are given;In chapter 3,a priori estimates of the solutions for prescribed curvature equation are mainly established.In chapter 4,we give the proof of the main theorem.