The Convexity Of The Horizontal Line Of A Very Class-like Hypersurface In Minkowski Space

For partial differential equations of the geometric properties and related research level sets,we can start from two aspects of quantitative and qualitative.For the maximal spacelike hypersurface defined on a convex ring in R2,we obtain the regularity and the strict convexity of its level lines by the continuity method,and the curvature estimate of the level lines is also derived.This paper will be divided into five sections-introduction: the equation of maximal space-like graph,a constant rank theorem,strict convexity of level lines,curvature estimate of level lines.In section 2,we firstly introduce the fundamental point of the maximal surface equation.In section 3,we recommend a powerful tool to study convexity problems-constant rank theorem.In section 4,we come to discuss the strict convexity of the level lines of the maximal spacelike hypersurface.In section 5,we will give a theorem of curvature estimate of the level lines of the maximal spacelike hypersurface,we will also make strict proof of this theorem.