Disjoint minimal graphs

TL;DR

This paper establishes an upper bound on the number of disjoint minimal graphs in n-dimensional space and confirms that in two dimensions, this number is at most three, approaching the conjectured maximum.

Contribution

The authors provide a new bound for the number of disjoint minimal graphs in any dimension and improve the known maximum in two dimensions.

Findings

Bound s(n) by e(n+1)^2 for n-dimensional space.

Proved s(2) ≤ 3, close to the conjectured maximum of 2.

Established new constraints on disjoint minimal graphs.

Abstract

We prove that the number s(n) of disjoint minimal graphs supported on domains in R^n is bounded by e(n+1)^2. In the two-dimensional case we show that s(2) is at most three (the conjectured number is two).