On S.L. Tabachnikov's conjecture

Details On S.L. Tabachnikov's conjecture On S.L. Tabachnikov's conjecture

2005-07-19

arxiv.org/abs/math/0507379v1

Mathematics

Metric Geometry

Scientific paper

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 $\Gamma\ne k\Gamma_1$. An inequality $T(\Gamma)\ge
T(\Gamma_1)$ is proved for curves in a hemisphere.

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