Interior curvature estimate for curvature quotient equations on convex hypersurfaces

TL;DR

This paper establishes interior curvature estimates for convex hypersurfaces satisfying a specific curvature quotient equation, advancing understanding of geometric properties and curvature bounds in differential geometry.

Contribution

It provides new interior curvature estimates for convex hypersurfaces solving the quotient curvature equation, a novel result in geometric analysis.

Findings

Derived interior curvature bounds for convex solutions

Extended curvature estimates to quotient equations

Enhanced understanding of geometric properties of convex hypersurfaces

Abstract

We study interior curvature estimates for convex graphs which satisfy the quotient equation $\frac{\sigma_{n}}{\sigma_{n-2}}(\lambda)=f(X)>0$ in this paper.