## Proceedings of the International Conference on Geometry, Integrability and Quantization

### Construction of Maximal Surfaces in the Lorentz-Minkowski Space

Pablo Mira

#### Abstract

The Björling problem for maximal surfaces in Lorentz–Minkowski space $\mathbb{L}^3$ has been recently studied by the author together with Alías and Chaves. The present paper is a natural extension of that work, and provides several variations of Björling problem. The main scheme is the following. One starts with a spacelike analytic curve in $\mathbb{L}^3$, and asks for the construction of a maximal surface which contains that curve, and satisfies additionally some other geometric condition. The solution of these Björling-type problems are then applied with a twofold purpose: to construct examples of maximal surfaces in $\mathbb{L}^3$ with prescribed properties, and to classify certain families of maximal surfaces.

#### Article information

Dates
First available in Project Euclid: 12 June 2015

https://projecteuclid.org/ euclid.pgiq/1434145480

Digital Object Identifier
doi:10.7546/giq-3-2002-337-350

Mathematical Reviews number (MathSciNet)
MR1884858

Zentralblatt MATH identifier
1019.53026

#### Citation

Mira, Pablo. Construction of Maximal Surfaces in the Lorentz-Minkowski Space. Proceedings of the Third International Conference on Geometry, Integrability and Quantization, 337--350, Coral Press Scientific Publishing, Sofia, Bulgaria, 2002. doi:10.7546/giq-3-2002-337-350. https://projecteuclid.org/euclid.pgiq/1434145480