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On asymptotic cones of surfaces with constant curvature and the third Painlevé equation

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Abstract:

It is shown that for any surface in ℝ3 with constant negative Gaussian curvature and two straight asymptotic lines there exists a cone such that the distances from all its points to the surface are bounded. Analytic and geometric descriptions of the cone are obtained. This cone is asymptotic also for constant mean curvature planes in ℝ3 with inner rotational symmetry.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Berlin, Straße des¶17. Juni 136, D-10623 Berlin, Germany. e-mail: bobenko@math.tu-berlin.de, , , , , , DE

    Alexander I. Bobenko

  2. Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191011, Russia, , , , , , RU

    Alexander V. Kitaev

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  1. Alexander I. Bobenko
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  2. Alexander V. Kitaev
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Received: 23 April 1998

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Bobenko, A., Kitaev, A. On asymptotic cones of surfaces with constant curvature and the third Painlevé equation. manuscripta math. 97, 489–516 (1998). https://doi.org/10.1007/s002290050117

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  • DOI: https://doi.org/10.1007/s002290050117

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