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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2004, Volume 247, Pages 182–185 (Mi tm16)  

This article is cited in 5 scientific papers (total in 5 papers)

Two Applications of Topology to Convex Geometry

L. Montejano

National Autonomous University of Mexico, Institute of Mathematics
Full-text PDF (124 kB) Citations (5)
References:
Abstract: The purpose of this paper is to prove two theorems of convex geometry using the techniques of topology. The first theorem states that if, for a strictly convex body $K$, one may choose continuously a centrally symmetric section, then $K$ must be centrally symmetric. The second theorem states that if every section of a three-dimensional convex body $K$ through the origin has an axis of symmetry, then there is a section of $K$ through the origin which is a disk.
Received in May 2004
Bibliographic databases:
UDC: 515.1
Language: English
Citation: L. Montejano, “Two Applications of Topology to Convex Geometry”, Geometric topology and set theory, Collected papers. Dedicated to the 100th birthday of professor Lyudmila Vsevolodovna Keldysh, Trudy Mat. Inst. Steklova, 247, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 182–185; Proc. Steklov Inst. Math., 247 (2004), 164–167
Citation in format AMSBIB
\Bibitem{Mon04}
\by L.~Montejano
\paper Two Applications of Topology to Convex Geometry
\inbook Geometric topology and set theory
\bookinfo Collected papers. Dedicated to the 100th birthday of professor Lyudmila Vsevolodovna Keldysh
\serial Trudy Mat. Inst. Steklova
\yr 2004
\vol 247
\pages 182--185
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm16}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2168169}
\zmath{https://zbmath.org/?q=an:1104.52001}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2004
\vol 247
\pages 164--167
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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