Uniform A Priori Estimates For A Class Of Horizontal Minimal Equations

TL;DR

This paper establishes uniform a priori estimates for a class of horizontal minimal equations in product spaces, leading to existence results in specific cases, advancing the understanding of minimal surface equations.

Contribution

It provides new uniform a priori estimates for horizontal minimal equations in product spaces, including boundary gradient and modulus of continuity, and proves existence in two-variable cases.

Findings

Established uniform C^0 horizontal length estimates

Derived uniform boundary gradient estimates

Proved existence results in two-variable cases

Abstract

In the product space H^n \times R; we obtain uniform a priori C^0 horizontal length estimates, uniform a priori C^1 boundary gradient estimates, as well as uniform modulus of continuity, for a class of horizontal minimal equations. In two independent variables, we derive a certain uniform global a priori C^1 estimates and we infer an existence result.