Prescribing singularities of maximal surfaces via a singular Björling representation formula

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19 Citations (Scopus)

Abstract

We derive a proper formulation of the singular Björling problem for spacelike maximal surfaces with singularities in the Lorentz-Minkowski 3-space which roughly asks whether there exists a maximal surface that contains a prescribed curve as singularities, and then provide a representation formula which solves the problem in an affirmative way. As consequences, we construct many kinds of singularities of maximal surfaces and deduce some properties of the maximal surfaces related to the singularities due to the geometry of the Gauss map.

Original languageEnglish
Pages (from-to)2167-2177
Number of pages11
JournalJournal of Geometry and Physics
Volume57
Issue number11
DOIs
Publication statusPublished - 2007 Oct

Keywords

  • Björling formula
  • Maximal surfaces
  • Singularities

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

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