Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T08:25:57.193Z Has data issue: false hasContentIssue false

Björling problem for maximal surfaces in Lorentz–Minkowski space

Published online by Cambridge University Press:  01 May 2003

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]

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
Copyright
2003 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)