Abstract:
Sharp estimates are obtained for the convex hulls of polygonal lines which are convex in Rn (i.e. which are cut by an arbitrary hyperplane no more than n times) and have segments of given length and number. The extremal polygonal lines are found.
Closed and open polygonal lines are considered. Passing to the limit yields the solution of similar problems for convex curves.
Bibliography: 13 titles.
Citation:
A. A. Nudelman, “Isoperimetric problems for the convex hulls of polygonal lines and curves in multidimensional spaces”, Math. USSR-Sb., 25:2 (1975), 276–294
\Bibitem{Nud75}
\by A.~A.~Nudelman
\paper Isoperimetric problems for the convex hulls of polygonal lines and curves in multidimensional spaces
\jour Math. USSR-Sb.
\yr 1975
\vol 25
\issue 2
\pages 276--294
\mathnet{http://mi.mathnet.ru/eng/sm3135}
\crossref{https://doi.org/10.1070/SM1975v025n02ABEH002209}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=375090}
\zmath{https://zbmath.org/?q=an:0308.52012}
Linking options:
https://www.mathnet.ru/eng/sm3135
https://doi.org/10.1070/SM1975v025n02ABEH002209
https://www.mathnet.ru/eng/sm/v138/i2/p294
This publication is cited in the following 5 articles:
Tilli P., “Isoperimetric Inequalities for Convex Hulls and Related Questions”, Trans. Am. Math. Soc., 362:9 (2010), 4497–4509
Pech P., “On the Need of Radical Ideals in Automatic Proving: a Theorem About Regular Polygons”, Automated Deduction in Geometry, Lecture Notes in Artificial Intelligence, 4869, eds. Botana F., Recio T., Springer-Verlag Berlin, 2007, 157–170
Faybusovich L., Gekhtman M., “Calculation of Universal Barrier Functions for Cones Generated by Chebyshev Systems Over Finite Sets”, SIAM J. Optim., 14:4 (2004), 965–979
Vyacheslav Sedykh, Boris Shapiro, “On Young hulls of convex curves in ?2n”, J Geom, 63:1-2 (1998), 168
John André Wieacker, “Geometric Inequalities for Random Surfaces”, Math Nachr, 142:1 (1989), 73
Citation in format AMSBIB
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