The moduli space of embedded singly periodic maximal surfaces with isolated singularities in the Lorentz-Minkowski space $\l^3$

TL;DR

This paper characterizes the moduli space of singly periodic maximal surfaces with isolated singularities in Lorentz-Minkowski space, showing it forms a real analytic manifold of specific dimension and topology.

Contribution

It establishes that the moduli space of such maximal surfaces is a real analytic manifold with a precise dimension and topology, under natural normalizations.

Findings

Moduli space is a real analytic manifold of dimension 3n+4.

Topology matches uniform convergence of graphs on compact subsets.

Results apply to surfaces with finite singularities.

Abstract

We show that, up to some natural normalizations, the moduli space of singly periodic complete embedded maximal surfaces in the Lorentz-Minkowski space $\l^3=(\r^3,dx_1^2+dx_2^2-dx_3^2),$ with fundamental piece having a finite number $(n+1)$ of singularities, is a real analytic manifold of dimension $3n+4.$ The underlying topology agrees with the topology of uniform convergence of graphs on compact subsets of $\{x_3=0\}.$