Research Papers

On the total curvature of minimizing geodesics on convex surfaces

N. Lebedeva^ab, A. Petrunin<sup>c

a</sup> Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskii pr., 28, 198504, St. Petersburg, Russia
^b St. Petersburg Branch, Steklov Institute of Mathematics, Russian Academy of Sciences, Fontanka, 27, 191023, St. Petersburg, Russia
^c Math. Dept. PSU, University Park, PA 16802, USA

Abstract: We give a universal upper bound for the total curvature of a minimizing geodesic on a convex surface in the Euclidean space.

Keywords: geodesic, curvature, Liberman's lemma, development, tongue.

Received: 20.05.2016

Language: English

 English version: St. Petersburg Mathematical Journal, 2018, 29:1, 139–153

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