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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



On the total curvature of minimizing geodesics on convex surfaces

Authors: N. Lebedeva and A. Petrunin
Original publication: Algebra i Analiz, tom 29 (2017), nomer 1.
Journal: St. Petersburg Math. J. 29 (2018), 139-153
MSC (2010): Primary 53C21
Published electronically: December 27, 2017
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Abstract: A universal upper bound is given for the total curvature of a minimizing geodesic on a convex surface in the Euclidean space.

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Additional Information

N. Lebedeva
Affiliation: Department of Mathematics and Mechanics St. Petersburg State University Universitetskii pr. 28 198504 St. Petersburg Russia; St. Petersburg Branch Steklov Institute of Mathematics Russian Academy of Sciences Fontanka 27 191023 St. Petersburg Russia

A. Petrunin
Affiliation: Department of Mathematics Pennsylvania State University University Park, PA 16802 USA

Keywords: Geodesic, curvature, Liberman's lemma, development, tongue
Received by editor(s): May 20, 2016
Published electronically: December 27, 2017
Additional Notes: N. Lebedeva was partially supported by RFBR grant 14-01-00062. A. Petrunin was partially supported by NSF grant DMS 1309340
Dedicated: Dedicated to Yu. D. Burago on the occasion of his 80th birthday
Article copyright: © Copyright 2017 American Mathematical Society

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