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A halfspace theorem for proper, negatively curved immersions

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Abstract

Generalizing the classical halfspace theorem for minimal surfaces (Hoffman and Meeks in Invent Math 101:373–377, 1990), we prove such a result for two-dimensional surfaces in \({\mathbb{R}^3}\) of negative Gaussian curvature. Instead of requiring an elliptic differential equation, we merely assume some inequality involving the principal curvatures of the surface to be satisfied, see assumption (1). Surfaces of this type arise naturally as critical points of weighted area functionals defined in (2).

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  1. Institut für Differentialgeometrie, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    Matthias Bergner

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  1. Matthias Bergner
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Correspondence to Matthias Bergner.

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Bergner, M. A halfspace theorem for proper, negatively curved immersions. Ann Glob Anal Geom 38, 191–199 (2010). https://doi.org/10.1007/s10455-010-9208-2

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  • DOI: https://doi.org/10.1007/s10455-010-9208-2

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