Geodesic
On Tabachnikov's conjecture
Algebra i analiz, Tome 19 (2007) no. 1, pp. 177-193.

Voir la notice de l'article provenant de la source Math-Net.Ru

Tabachnikov's conjecture is proved: for any closed curve $\Gamma$ lying inside aЁconvex closed curve $\Gamma_1$ the mean absolute curvature $T(\Gamma)$ exceeds $T(\Gamma_1)$ if $\Gamma\ne k\Gamma_1$.
Keywords: Geometric inequalities, mean absolute curvature, convexity. 
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A. I. Nazarov; F. V. Petrov. On Tabachnikov's conjecture. Algebra i analiz, Tome 19 (2007) no. 1, pp. 177-193. http://geodesic.mathdoc.fr/item/AA_2007_19_1_a7/

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