The moduli space of embedded singly periodic maximal surfaces with isolated singularities in the Lorentz–Minkowski space $mathbb{L}^3$

摘要

We show that, up to some natural normalizations, the moduli space of singly periodic complete embedded maximal surfaces in the Lorentz–Minkowski space $mathbb{L}^3=big(mathbb{R}^3, dx_1^2+dx_2^2-dx_3^2big)$ , 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}.