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Björling problem for maximal surfaces in Lorentz–Minkowski space

Published online by Cambridge University Press:  01 May 2003

LUIS J. ALÍAS ,
ROSA M. B. CHAVES  and
PABLO MIRA
LUIS J. ALÍAS
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, E-30100 Espinardo, Murcia, Spain. e-mail: [email protected]
ROSA M. B. CHAVES
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, 05315-970 São Paulo–SP, Brazil. e-mail: [email protected]
PABLO MIRA
Affiliation:
Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, E-30203 Cartagena, Murcia, Spain. e-mail: [email protected]
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Abstract

We introduce a new approach to the local study of maximal surfaces in Lorentz–Minkowski space, based on a complex representation formula for this kind of surfaces. As an application we solve a certain Björling-type problem in Lorentz–Minkowski space and we obtain some results related to it. We also establish, springing from this complex representation, a way of introducing examples of maximal surfaces with interesting prescribed geometric properties. Further applications of the complex representation let us inspect some known results from a different perspective, and show how our approach can be used to classify certain families of maximal surfaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 134 , Issue 2 , March 2003 , pp. 289 - 316
Copyright
2003 Cambridge Philosophical Society

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