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Algebra i Analiz, 2007, Volume 19, Issue 1, Pages 177–193 (Mi aa107)  
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
Full-text PDF (188 kB) Citations (4)
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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
English version:
St. Petersburg Mathematical Journal, 2008, Volume 19, Issue 1, Pages 125–135
DOI: https://doi.org/10.1090/S1061-0022-07-00989-2
Bibliographic databases:
Document Type: Article
MSC: Primary 53A04; Secondary 52A40, 52A10
Language: Russian
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
Citation in format AMSBIB
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\paper On Tabachnikov's conjecture
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\transl
\jour St. Petersburg Math. J.
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\issue 1
\pages 125--135
\crossref{https://doi.org/10.1090/S1061-0022-07-00989-2}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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