On S.L. Tabachnikov's conjecture
classification
🧮 math.MG
keywords
gammaclosedconjecturecurveprovedtabachnikovabsoluteconvex
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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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