Asymptotic behavior at infinity of Weingarten surfaces

TL;DR

This paper investigates the asymptotic behavior of Weingarten surfaces with finite total curvature in three-dimensional space, establishing their behavior at infinity and solving related boundary value problems.

Contribution

It provides the first detailed asymptotic expansion at infinity for these surfaces and solves the Dirichlet problem for elliptic Weingarten equations in convex domains.

Findings

Derived asymptotic expansion at infinity for embedded ends

Established a maximum principle at infinity

Solved the Dirichlet problem for elliptic Weingarten equations

Abstract

We derive the asymptotic expansion at infinity for embedded ends of uniformly elliptic Weingarten surfaces with finite total curvature in $\mathbb{R}^3$, and we establish a maximum principle at infinity. Furthermore, we solve the Dirichlet problem for the uniformly elliptic Weingarten equation in dimension two on strictly convex bounded domains.