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ON THE GAUSSIAN CURVATURE OF MAXIMAL SURFACES AND THE CALABI–BERNSTEIN THEOREM

Published online by Cambridge University Press:  25 July 2001

LUIS J. ALÍAS  and
BENNETT PALMER
LUIS J. ALÍAS
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, E-30100 Espinardo, Murcia, Spain; ljalias@um.es
BENNETT PALMER
Affiliation:
Department of Mathematical Sciences, University of Durham, Durham DH1 3LE; bennett.palmer@durham.ac.uk
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Abstract

In this paper, a new approach to the Calabi–Bernstein theorem on maximal surfaces in the Lorentz– Minkowski space L3 is introduced. The approach is based on an upper bound for the total curvature of geodesic discs in a maximal surface in L3, involving the local geometry of the surface and its hyperbolic image. As an application of this, a new proof of the Calabi–Bernstein theorem is provided.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 4 , July 2001 , pp. 454 - 458
Copyright
© The London Mathematical Society 2001

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