The space of complete embedded maximal surfaces with isolated singularities in the 3-dimensional Lorentz-Minkowski space $ł^3$

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dc.creatorFernandez, Isabel
dc.creatorLopez, Francisco J.
dc.creatorSouam, Rabah
dc.date2003-11-19
dc.date2005-01-27
dc.date.accessioned2026-07-07T05:03:03Z
dc.date.available2026-07-07T05:03:03Z
dc.descriptionWe show that a complete embedded maximal surface in the 3-dimensional Lorentz-Minkowski space $L^3$ with a finite number of singularities is, up to a Lorentzian isometry, an entire graph over any spacelike plane asymptotic to a vertical half catenoid or a horizontal plane and with conelike singular points. We study the space $G_n$ of entire maximal graphs over $\{x_3=0\}$ in $L^3$ with $n+1 \geq 2$ conelike singularities and vertical limit normal vector at infinity. We show that $G_n$ is a real analytic manifold of dimension $3n+4,$ and the coordinates are given by the position of the singular points in $R^3$ and the logarithmic growth at the end. We also introduce the moduli space $M_n$ of {\em marked} graphs with $n+1$ singular points (a mark in a graph is an ordering of its singularities), which is a $(n+1)$-sheeted covering of $G_n.$ We prove that identifying marked graphs differing by translations, rotations about a vertical axis, homotheties or symmetries about a horizontal plane, the corresponding quotient space $M_n$ is an analytic manifold of dimension $3n-1.$
dc.description32 pages, 4 figures, corrected typos, former Theorem 3.3 (now Theorem 2.2) modified
dc.identifierhttps://arxiv.org/abs/math/0311330
dc.identifierhttp://arxiv.org/abs/math/0311330
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69257
dc.subjectDifferential Geometry
dc.subject53C50; 58D10; 53C42
dc.titleThe space of complete embedded maximal surfaces with isolated singularities in the 3-dimensional Lorentz-Minkowski space $ł^3$
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