[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