Double-periodic maximal surfaces with singularities

TL;DR

This paper constructs a family of double-periodic maximal surfaces with singularities, exploring their geometric properties and classification based on the generating matrices, contributing to the understanding of maximal surface solutions.

Contribution

It introduces a new family of double-periodic maximal surfaces parameterized by generating matrices, analyzing their singularities and space-like or mixed types.

Findings

Solutions are either space-like or of mixed type.

Singularities are isolated and of light-cone type.

Parameterization by a submanifold of 3x3 matrices.

Abstract

We construct and study a family of double-periodic almost entire solutions of the maximal surface equation. The solutions are parameterized by a submanifold of $3\times 3$-matrices (the so-called generating matrices). We show that the constructed solutions are either space-like or of mixed type with the light-cone type isolated singularities.