2004/12/22 by Isabel Fernández, Isabel Fernandez, Francisco J. López +3
Mathematics · #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities #Primary 53C50 #Secondary 53C42 #math.DG #msc:53A10 #msc:53C42 #msc:53C50
paper · pdf · doi:10.48550/arxiv.math/0412461
27 pages, corrected typos, Lemma 2.5 and Theorem 4.1 changed
openalex publication_date 2004/12/22 · arxiv created 2005/01/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A maximal surface \sb with isolated singularities in a complete flat Lorentzian 3-manifold \N is said to be entire if it lifts to a (periodic) entire multigraph \sb in ł3. In addition, \sb is called of finite type if it has finite topology, finitely many singular points and \sb is finitely sheeted. Complete and proper maximal immersions with isolated singularities in \N are entire, and entire embedded maximal surfaces in \N with a finite number of singularities are of finite type. We classify complete flat Lorentzian 3-manifolds carrying entire maximal surfaces of finite type, and deal with the topology, Weierstrass representation and asymptotic behavior of this kind of surfaces. Finally, we construct new examples of periodic entire embedded maximal surfaces in ł3 with fundamental piece having finitely many singularities.