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Extremal convex sets. (English) Zbl 0513.52003

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
52A40 Inequalities and extremum problems involving convexity in convex geometry
52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
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[1] Alexander, R.: The width and diameter of a simplex. Geom. Dedic.6, 87-94 (1977). · Zbl 0372.52003 · doi:10.1007/BF00181583
[2] Bonnesen, T., Fenchel, W.: Theorie der konvexen Körper. Berlin: Springer. 1934. · Zbl 0008.07708
[3] Eggleston, H. G.: Convexity. Cambridge: University Press. 1958.
[4] Eggleston, H. G.: Sets of constant width in finite dimensional Banach spaces. Israel J. Math.3, 163-172 (1965). · Zbl 0166.17901 · doi:10.1007/BF02759749
[5] Fejes Toth, L.: Lagerungen in der Ebene, auf der Kugel und im Raum. 2. Aufl. Berlin-Heidelberg-New York: Springer. 1972.
[6] Groemer, H.: Existenzsätze für Lagerungen im Euklidischen Raum. Math. Z.81, 260-278 (1963). · Zbl 0123.39104 · doi:10.1007/BF01111546
[7] Gruber, P. M., Schneider, R.: Problems in geometric convexity. In: Contributions to Geometry. Proc. Geom. Sympos., Siegen 1978, pp. 258-278. Basel-Boston-Stuttgart: Birkhäuser. 1979.
[8] Hans, R. J.: Extremal packing and covering sets. Mh. Math.71, 203-213 (1967). · Zbl 0158.19604 · doi:10.1007/BF01298325
[9] Heil, E.: Kleinste konvexe Körper gegebener Dicke. Preprint Nr. 453. Fachbereich Mathematik, Technische Hochschule Darmstadt. 1978.
[10] Jung, H.::Uber die kleinste Kugel, die eine räumliche Figur einschließt. J. reine angew. Math.123, 241-257 (1901). · JFM 32.0296.05 · doi:10.1515/crll.1901.123.241
[11] Lekkerkerker, C. G.: Geometry of Numbers. Amsterdam-London: North Holland. 1969. · Zbl 0198.38002
[12] Steinhagen, P.: Über die größte Kugel in einer konvexen Punktmenge. Abh. Math. Sem. Hamburg Univ.1, 15-26 (1922). · JFM 48.0837.03 · doi:10.1007/BF02940577
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