The number of conformally equivalent maximal graphs

TL;DR

This paper demonstrates that the count of conformally equivalent entire maximal graphs with finitely many singularities is a universal constant depending solely on the number of singularities, providing explicit descriptions for certain configurations.

Contribution

It establishes a universal constant for the number of conformally equivalent maximal graphs with singularities and describes their structure explicitly.

Findings

Number of conformally equivalent graphs is 2^n for n+1 singularities.

Provides explicit descriptions of graphs with singularities on a plane orthogonal to the limit normal.

Shows the count depends only on the number of singularities.

Abstract

We show that the number of entire maximal graphs with finitely many singular points that are conformally equivalent is a universal constant that depends only on the number of singularities, namely 2^$ for graphs with n+1 singularities. We also give an explicit description of the family of entire maximal graphs with a finite number of singularities all of them lying on a plane orthogonal to the limit normal vector at infinity.