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On the affine Bernstein problem

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Abstract

A partial solution to the affine Bernstein problem is given. The elliptic paraboloid is characterized as a locally strongly convex, affine complete, affine-maximal surface in A 3, satisfying a certain growth condition, about its affine Gauss-Kronecker curvature.

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Authors and Affiliations

  1. Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    A. Martínez & F. Milán

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  1. A. Martínez
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  2. F. Milán
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Research partially supported by DGICYT Grant PS87-0115-CO3-02.

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Martínez, A., Milán, F. On the affine Bernstein problem. Geom Dedicata 37, 295–302 (1991). https://doi.org/10.1007/BF00181405

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  • DOI: https://doi.org/10.1007/BF00181405

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