English

On S.L. Tabachnikov's conjecture

Metric Geometry 2007-05-23 v1

Abstract

S. L. Tabachnikov's conjecture is proved: for any closed curve Γ\Gamma lying inside convex closed curve Γ1\Gamma_1 the mean absolute curvature T(Γ)T(\Gamma) exceeds T(Γ1)T(\Gamma_1) if ΓkΓ1\Gamma\ne k\Gamma_1. An inequality T(Γ)T(Γ1)T(\Gamma)\ge T(\Gamma_1) is proved for curves in a hemisphere.

Keywords

Cite

@article{arxiv.math/0507379,
  title  = {On S.L. Tabachnikov's conjecture},
  author = {A. I. Nazarov and F. V. Petrov},
  journal= {arXiv preprint arXiv:math/0507379},
  year   = {2007}
}