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This article is cited in 4 scientific papers (total in 4 papers)
Research Papers
On Tabachnikov's conjecture
A. I. Nazarova, F. V. Petrovb a St. Petersburg State University, Department of Mathematics and Mechanics
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
Tabachnikov's conjecture is proved: for any closed curve $\Gamma$ lying inside aЁconvex closed curve $\Gamma_1$ the mean absolute curvature $T(\Gamma)$ exceeds $T(\Gamma_1)$ if $\Gamma\ne k\Gamma_1$.
Keywords:
Geometric inequalities, mean absolute curvature, convexity.
Received: 01.08.2006
Citation:
A. I. Nazarov, F. V. Petrov, “On Tabachnikov's conjecture”, Algebra i Analiz, 19:1 (2007), 177–193; St. Petersburg Math. J., 19:1 (2008), 125–135
Linking options:
https://www.mathnet.ru/eng/aa107 https://www.mathnet.ru/eng/aa/v19/i1/p177
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Abstract page: | 647 | Full-text PDF : | 268 | References: | 43 | First page: | 10 |
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