ar X iv : m at h / 04 12 46 1 v 3 [ m at h . D G ] 1 7 Ja n 20 05 Periodic Maximal surfaces in the Lorentz - Minkowski space
نویسندگان
چکیده
A maximal surface S with isolated singularities in a complete flat Lorentzian 3-manifold N is said to be entire if it lifts to a (periodic) entire multigraph S̃ in L. In addition, S is called of finite type if it has finite topology, finitely many singular points and S̃ is a finitely sheeted multigraph. Complete (or 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 L with fundamental piece having finitely many singularities.
منابع مشابه
ar X iv : 0 70 7 . 19 46 v 1 [ m at h . D G ] 1 3 Ju l 2 00 7 The uniqueness of the helicoid in the Lorentz - Minkowski space
We prove that the Lorentzian helicoid and Enneper’s surface are the unique properly embedded maximal surfaces bounded by a lightlike regular arc of mirror symmetry.
متن کاملar X iv : m at h / 05 01 45 4 v 1 [ m at h . A G ] 2 5 Ja n 20 05 HIGHER NOETHER - LEFSCHETZ LOCI OF ELLIPTIC SURFACES
We calculate the dimension of the locus of elliptic surfaces over P 1 with a section and a given Picard number, in the corresponding moduli space.
متن کاملar X iv : m at h / 04 01 12 6 v 1 [ m at h . N T ] 1 3 Ja n 20 04 THREE LECTURES ON THE RIEMANN ZETA - FUNCTION
متن کامل
ar X iv : m at h / 04 10 33 5 v 2 [ m at h . C O ] 3 1 Ja n 20 05 HIGHER CONNECTIVITY OF GRAPH COLORING COMPLEXES
The main result of this paper is a proof of the following conjecture of Babson & Kozlov: Theorem. Let G be a graph of maximal valency d, then the complex Hom (G, Kn) is at least (n − d − 2)-connected. Here Hom (−,−) denotes the polyhedral complex introduced by Lovász to study the topological lower bounds for chromatic numbers of graphs. We will also prove, as a corollary to the main theorem, th...
متن کاملar X iv : m at h / 05 01 45 4 v 2 [ m at h . A G ] 1 2 Ja n 20 06 HIGHER NOETHER - LEFSCHETZ LOCI OF ELLIPTIC SURFACES
We calculate the dimension of the locus of Jacobian elliptic surfaces over P with given Picard number, in the corresponding moduli space.
متن کامل