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Zapiski Nauchnykh Seminarov POMI, 2005, Volume 329, Pages 28–55 (Mi znsl293)  
This article is cited in 8 scientific papers (total in 8 papers)

An isoperimetric problem for tetrahedra

V. A. Zalgaller

Weizmann Institute of Science
Full-text PDF (449 kB) Citations (8)
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Abstract: It is proved that a regular tetrahedron has the maximal possible surface area among tetrahedra with unit geodesic diameter of surface. An independent proof of O'Rourk–Schevon's theorem about polar points on a convex polyhedron is given. A. D. Aleksandrov's general problem on the area of a convex surface with fixed geodesic diameter is dicussed.
Received: 23.11.2005
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 140, Issue 4, Pages 511–527
DOI: https://doi.org/10.1007/s10958-007-0431-8
Bibliographic databases:
UDC: 514.113
Language: Russian
Citation: V. A. Zalgaller, “An isoperimetric problem for tetrahedra”, Geometry and topology. Part 9, Zap. Nauchn. Sem. POMI, 329, POMI, St. Petersburg, 2005, 28–55; J. Math. Sci. (N. Y.), 140:4 (2007), 511–527
Citation in format AMSBIB
\Bibitem{Zal05}
\by V.~A.~Zalgaller
\paper An isoperimetric problem for tetrahedra
\inbook Geometry and topology. Part~9
\serial Zap. Nauchn. Sem. POMI
\yr 2005
\vol 329
\pages 28--55
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl293}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2215329}
\zmath{https://zbmath.org/?q=an:1151.52309}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 140
\issue 4
\pages 511--527
\crossref{https://doi.org/10.1007/s10958-007-0431-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33845773950}
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  • https://www.mathnet.ru/eng/znsl/v329/p28
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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