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Zapiski Nauchnykh Seminarov POMI, 2001, Volume 280, Pages 234–238 (Mi znsl1482)  
This article is cited in 2 scientific papers (total in 2 papers)

A kinematic formula for affine diameters and affine medians of a convex set

V. V. Makeev

St. Petersburg State University, Department of Mathematics and Mechanics
Full-text PDF (120 kB) Citations (2)
Abstract: For a planar convex set $K$ with $C^2$-smooth boundary, the area of the set of the points lying on a given number of affine diameters of $K$ is estimated. As a corollary, it is proved that the area of $K$ is at most $\pi M^2/4$, where $M$ is the largest length of a chord of $K$ halving the area of $K$.
Received: 25.12.2000
English version:
Journal of Mathematical Sciences (New York), 2004, Volume 119, Issue 2, Pages 257–259
DOI: https://doi.org/10.1023/B:JOTH.0000008767.34024.40
Bibliographic databases:
UDC: 514.172
Language: Russian
Citation: V. V. Makeev, “A kinematic formula for affine diameters and affine medians of a convex set”, Geometry and topology. Part 7, Zap. Nauchn. Sem. POMI, 280, POMI, St. Petersburg, 2001, 234–238; J. Math. Sci. (N. Y.), 119:2 (2004), 257–259
Citation in format AMSBIB
\Bibitem{Mak01}
\by V.~V.~Makeev
\paper A kinematic formula for affine diameters and affine medians of a convex set
\inbook Geometry and topology. Part~7
\serial Zap. Nauchn. Sem. POMI
\yr 2001
\vol 280
\pages 234--238
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1482}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1879269}
\zmath{https://zbmath.org/?q=an:1078.52504}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2004
\vol 119
\issue 2
\pages 257--259
\crossref{https://doi.org/10.1023/B:JOTH.0000008767.34024.40}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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