Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 315

On Asymptotic Cones of Surfaces with Constant Curvature and the Third Painlevé Equation

A. I. Bobenko and A. V. Kitaev

Manuscripta math. 97 (1998) 489-516

It is shown that for any surface in $R^3$ 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 $R^3$ with inner rotational symmetry.

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