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

Source
Proceedings of the Third International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Gregory L. Naber, eds. (Sofia: Coral Press Scientific Publishing, 2002), 337-350

Dates
First available in Project Euclid: 12 June 2015

Permanent link to this document
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


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