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Curvature estimates for immersions of minimal surface type via uniformization and theorems of Bernstein type

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Abstract

We give an adequate parametric description of surfaces of minimal surface type, satisfying the weighted relation ϱ1κ1+ϱ2κ2 with the positive factors ϱ j for their principal curvatures κ j , by the introduction of weighted conformal parameters. We then establish apriori estimates of the principal curvatures for certain classes of surfaces. These estimates imply new theorems of Bernstein type.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik der Universität Bonn, Sonderforschungsbereich 256 Beringstraße 4, D-5300, Bonn 1, Bundesrepublik Deutschland

    Friedrich Sauvigny

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  1. Friedrich Sauvigny
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This paper is a part of the author’s Habilitationsschrift [S1] accepted by the Fachbereich Mathematik der Georg-August-Universität, Göttingen.

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Sauvigny, F. Curvature estimates for immersions of minimal surface type via uniformization and theorems of Bernstein type. Manuscripta Math 67, 69–97 (1990). https://doi.org/10.1007/BF02568423

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  • DOI: https://doi.org/10.1007/BF02568423

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