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VOL. 3 | 2002 Construction of Maximal Surfaces in the Lorentz-Minkowski Space


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.


Published: 1 January 2002
First available in Project Euclid: 12 June 2015

zbMATH: 1019.53026
MathSciNet: MR1884858

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

Rights: Copyright © 2002 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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