Prescribing singularities of maximal surfaces via a singular Björling representation formula

Research output: Contribution to journalArticle

18 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 1

Fingerprint

Maximal Surfaces
Representation Formula
Singularity
Spacelike Surface
Gauss Map
Singular Problems
Deduce
formulations
Curve
Formulation
curves
geometry

Keywords

  • Björling formula
  • Maximal surfaces
  • Singularities

ASJC Scopus subject areas

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

Cite this

@article{07112e1575954da897e276725333f0ff,
title = "Prescribing singularities of maximal surfaces via a singular Bj{\"o}rling representation formula",
abstract = "We derive a proper formulation of the singular Bj{\"o}rling 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.",
keywords = "Bj{\"o}rling formula, Maximal surfaces, Singularities",
author = "Kim, {Young Wook} and Seong-Deog Yang",
year = "2007",
month = "10",
day = "1",
doi = "10.1016/j.geomphys.2007.04.006",
language = "English",
volume = "57",
pages = "2167--2177",
journal = "Journal of Geometry and Physics",
issn = "0393-0440",
publisher = "Elsevier",
number = "11",

}

TY - JOUR

T1 - Prescribing singularities of maximal surfaces via a singular Björling representation formula

AU - Kim, Young Wook

AU - Yang, Seong-Deog

PY - 2007/10/1

Y1 - 2007/10/1

N2 - 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.

AB - 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.

KW - Björling formula

KW - Maximal surfaces

KW - Singularities

UR - http://www.scopus.com/inward/record.url?scp=35548936260&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35548936260&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2007.04.006

DO - 10.1016/j.geomphys.2007.04.006

M3 - Article

VL - 57

SP - 2167

EP - 2177

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

IS - 11

ER -