Two dimensional disjoint minimal graphs

TL;DR

This paper proves Meeks' conjecture that in three-dimensional space, there can be at most two disjoint minimal graphs supported in the same space, assuming the Gauss curvature tends to zero at infinity.

Contribution

It establishes a proof for Meeks' conjecture regarding the maximum number of disjoint minimal graphs in  under specific curvature conditions, advancing understanding of minimal surface configurations.

Findings

Maximum of two disjoint minimal graphs in  with zero Gauss curvature at infinity

Proof of Meeks' conjecture under specified curvature assumptions

Enhanced understanding of the structure of minimal surfaces in 

Abstract

In this paper, under the assumption of Gauss curvature vanishing at infinity, we will prove Meeks' conjecture: the number of disjointly supported minimal graphs in $\mathbb{R}^3$ is at most two.