### 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 language | English |
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Pages (from-to) | 2167-2177 |

Number of pages | 11 |

Journal | Journal of Geometry and Physics |

Volume | 57 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2007 Oct 1 |

### Fingerprint

### Keywords

- Björling formula
- Maximal surfaces
- Singularities

### ASJC Scopus subject areas

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

### Cite this

**Prescribing singularities of maximal surfaces via a singular Björling representation formula.** / Kim, Young Wook; Yang, Seong-Deog.

Research output: Contribution to journal › Article

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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 -