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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 4, Pages 215–225 (Mi timm438)  

This article is cited in 2 scientific papers (total in 3 papers)

On construction of bodies of constant width containing a given set

E. S. Polovinkin

Moscow Institute of Physics and Technology

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.

Full text: PDF file (206 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, 269, suppl. 1, S247–S257

UDC: 517.977
Received: 14.08.2009

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{http://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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962343962}


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    This publication is cited in the following articles:
    1. Pedro Moreno J., Schneider R., “Lipschitz Selections of the Diametric Completion Mapping in Minkowski Spaces”, Adv. Math., 233:1 (2013), 248–267  crossref  mathscinet  zmath  isi  scopus
    2. Martini H., Papini P.L., Spirova M., “Complete Sets and Completion of Sets in Banach Spaces”, Mon.heft. Math., 174:4 (2014), 587–597  crossref  mathscinet  zmath  isi  scopus
    3. M. V. Balashov, O. V. Besov, B. I. Golubov, V. V. Goryainov, V. N. Diesperov, S. I. Dudov, G. E. Ivanov, S. P. Konovalov, R. V. Konstantinov, A. B. Kurzhanskii, S. R. Nasyrov, A. G. Sergeev, V. V. Starkov, V. M. Tikhomirov, M. I. Shabunin, “Evgenii Sergeevich Polovinkin (on his 70th birthday)”, Russian Math. Surveys, 71:5 (2016), 983–987  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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