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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 4, Pages 215–225 (Mi timm438)  

This article is cited in 3 scientific papers (total in 4 papers)

On construction of bodies of constant width containing a given set

E. S. Polovinkin

Moscow Institute of Physics and Technology
Full-text PDF (206 kB) Citations (4)
References:
Abstract: A survey of the author's results is presented, and the research is continued of the known differential geometry problem on the construction of bodies of constant width containing an arbitrary given bounded set of the same diameter as the width of the bodies. The problem is considered for sets from reflexive Banach spaces in which the unit ball is a generating set. Using earlier results in strongly convex analysis and an explicit formula for constructing one of such bodies of constant width, we establish a criteria for the uniqueness of the complement of an arbitrary set to a body of constant width and propose some algorithms for constructing all bodies of constant width that contain a given set.
Keywords: convex bodies of constant width, strongly convex analysis.
Received: 14.08.2009
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, Volume 269, Issue 1, Pages S247–S257
DOI: https://doi.org/10.1134/S0081543810060209
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: E. S. Polovinkin, “On construction of bodies of constant width containing a given set”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 4, 2009, 215–225; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S247–S257
Citation in format AMSBIB
\Bibitem{Pol09}
\by E.~S.~Polovinkin
\paper On construction of bodies of constant width containing a~given set
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 4
\pages 215--225
\mathnet{http://mi.mathnet.ru/timm438}
\elib{https://elibrary.ru/item.asp?id=12952767}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 269
\issue , suppl. 1
\pages S247--S257
\crossref{https://doi.org/10.1134/S0081543810060209}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962343962}
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  • https://www.mathnet.ru/eng/timm/v15/i4/p215
  • 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
    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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    Abstract page:616
    Full-text PDF :218
    References:82
    First page:4
     
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