The moduli space of embedded singly periodic maximal surfaces with isolated singularities in the Lorentz-Minkowski space ł³

2004/12/09 by Isabel Fernández, Isabel Fernandez, Francisco J. Lopez +5
Mathematics · #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #Primary 53C50 #Secondary 58D10 #math.DG #msc:53C42 #msc:53C50 #msc:58D10

paper · pdf · doi:10.48550/arxiv.math/0412190

26 pages, 4 figures

arxiv created 2004/12/09 · openalex publication_date 2004/12/09 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We show that, up to some natural normalizations, the moduli space of singly periodic complete embedded maximal surfaces in the Lorentz-Minkowski space ł³=(\r³,dx₁²+dx₂²-dx₃²), 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 \x₃=0\.

Citations

• Spacelike hypersurfaces with prescribed boundary values and mean curvature
• Maximal Space-like Hypersurfaces in the Lorentz-Minkowski Spaces

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