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On the Gaussian Curvature of Maximal Surfaces and the Calabi–Bernstein Theorem
Author(s) -
Alías Luis J.,
Palmer Bennett
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1017/s0024609301008220
Subject(s) - mathematics , gaussian curvature , minkowski space , geodesic , surface (topology) , lorentz transformation , constant mean curvature surface , minimal surface , curvature , upper and lower bounds , sectional curvature , space (punctuation) , hyperbolic space , pure mathematics , mathematical analysis , geometry , scalar curvature , classical mechanics , physics , linguistics , philosophy
In this paper, a new approach to the Calabi–Bernstein theorem on maximal surfaces in the Lorentz–Minkowski space L 3 is introduced. The approach is based on an upper bound for the total curvature of geodesic discs in a maximal surface in L 3 , 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.