Siberian Mathematical Journal

, Volume 42, Issue 5, pp 833–845 | Cite as

Estimation of the Length of a Simple Geodesic on a Convex Surface

  • V. A. Vaigant
  • O. Yu. Matukevich


It was proved by I. M. Liberman that for a C2-smooth closed surface M of positive Gaussian curvature there exists a number l such that any geodesic arc on M of length at least l is not simple. In this article we indicate a lower bound for l. We exhibit an example showing that our estimate is unimprovable.


Gaussian Curvature Convex Surface Positive Gaussian Curvature Simple Geodesic 
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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • V. A. Vaigant
    • 1
  • O. Yu. Matukevich
    • 2
  1. 1.Munster UniversityMunster
  2. 2.The Altai State UniversityBarnaul

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