[Authors]
 Nazarov A. I., Petrov F. V.

[Title]
 On S. L. Tabachnikov's conjecture

[AMS Subj-class]
 52A38 Length, area, volume
 52A40 Inequalities and extremum problems

[Keywords]
 closed curve, curvature, integral geometric inequalities

[Abstract]
 S. L. Tabachnikov's conjecture is proved: for any closed curve $\Gamma$
 lying inside convex closed curve $\Gamma_1$ the mean absolute curvature
 $T(\Gamma)$ exceeds $T(\Gamma_1)$ if $\Gamma\ne k\Gamma_1$.

[Comments]
 LaTeX, Russian, 13 pp.

[Contact e-mail]
 an@an4751.spb.edu
 fedorpetrov@mail.ru