On S.L. Tabachnikov's conjecture
Nazarov, A. I. · Petrov, F. V.
Original · EN
S. L. Tabachnikov's conjecture is proved: for any closed curve Γ lying inside convex closed curve Γ₁ the mean absolute curvature T(Γ) exceeds T(Γ₁) if Γ≠ kΓ₁. An inequality T(Γ)≥ T(Γ₁) is proved for curves in a hemisphere.
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