Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-13T06:46:46.292Z Has data issue: false hasContentIssue false
  • English
  • Français

Centrally symmetric convex sets and mixed volumes

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

P. R. Goodey
P. R. Goodey
Affiliation:
Department of Mathematics, Royal Holloway College, Englefield Green, Surrey.
Get access

Extract

Let denote the class of all compact convex sets in Euclidean n-dimensional space En, and let y be the collection of those members of k which are centrally symmetric. The topology in is that induced by the Hausdorff metric.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 24 , Issue 2 , December 1977 , pp. 193 - 198
Copyright
Copyright © University College London 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Alexandrav, A. D.. Über die Frage nach der Existenz eines konvexen Kôrpers, bei dem die Summe der Hauptkrümmungsradien eine gegebene positive Funktion ist, welche den Bedingungen der Geschlossenheit gentügt, Dokl. Akad. Nauk SSSR, 14 (1937), 59–60.Google Scholar
2.Blaschke, W.. Kreis und Kugel (Veh, Leipzig, 1916. Reprint: Chelsea, New York, 1948).Google Scholar
3.Bonnesen, T. and Fenchel, W.. Theorie der konvexen Korper, (Berlin, 1934).Google Scholar
4.Busemann, H.. Convex surfaces, (New York, 1958).Google Scholar
5.Erdélyi, A.et al., Bateman manuscript project. Higher transcendental functions II (New York- Toronto-London, 1953).Google Scholar
6.Firey, W. J.. “Blaschke sums of convex bodies and mixed bodies”, Proc. Colloquium on Convexity, Copenhagen, (1965), 94–101.Google Scholar
7.Schneider, R.. “Zu einem Problem von Shephard über die Projektionen konvexer Kôrper”, Math. Zeit., 101 (1967), 71–82.Google Scholar
8.Schneider, R.. “Über eine Integralgleichung in der Theorie der konvexen Kôrper”, Math. Nachr., 44 (1970), 55–75.CrossRefGoogle Scholar
9.Weil, W.. “Kontinuerliche Linearkombination von Strecken”, Math. Zeit., 148 (1976), 71–84.Google Scholar
10.Weil, W.. “Centrally symmetric convex bodies and distributions”, Israel Jour. Math., 24 (1976), 352–367.Google Scholar