The interior $C^2$ estimate for prescribed Gauss curvature equation in dimension two

TL;DR

This paper develops a new auxiliary function to establish interior second derivative estimates for the prescribed Gauss curvature equation specifically in two dimensions, advancing the understanding of curvature equations.

Contribution

The paper introduces a novel auxiliary function to prove interior $C^2$ estimates for the prescribed Gauss curvature equation in two dimensions, providing a new analytical tool.

Findings

Established interior $C^2$ estimates for the equation in 2D

Introduced a new auxiliary function for curvature estimates

Enhanced analytical techniques for prescribed curvature equations

Abstract

In this paper, we introduce a new auxiliary function, and establish the interior $C^2$ estimate for prescribed Gauss curvature equation in dimension two.