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About the centroid blody and the ellipsoid of inertia

Published online by Cambridge University Press:  26 February 2010

T. Bisztriczky  and
K. Böröczky Jr.
T. Bisztriczky
Affiliation:
Department of Mathematics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4. E-mail: tbisztri@math.ucalgary.ca.
K. Böröczky Jr.
Affiliation:
Renyi Institute of Mathematics, Budapest Pf. 127, H-1364 Hungary. E-mail: carlos@math-inst.hu
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Extract

The centroid body. Recall that the support function of a compact convex set K is denned to be hK(u) = maxxΣk: {<u, x>}. The support function hK is positive homogeneous and convex, and any function with these properties is the support function of some compact convex set (see the illuminating paper of Berger [2], or the classic [5] by Bonnesen and Fenchel).

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Type
Research Article
Information
Mathematika , Volume 48 , Issue 1-2 , December 2001 , pp. 1 - 13
Copyright
Copyright © University College London 2001

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References

1.Ball, K.. M.. An Elementary Introduction to Modern Convex Geometry (Cambridge University Press, Cambridge, 1997)Google Scholar
2.Berger, M.. Convexity. Amer. Math. Monthly, 97 (1990), 650–678.CrossRefGoogle Scholar
3.Blaschke, W.. Über affine Geometrie IX: verschiedene Bemerkungen und Aufgaben. Ber. Verh. Sächs. Akad. Wiss. Leipzig Math.-Phys. Kl. 69 (1917), 412–420.Google Scholar
4.Blaschke, W.. Über affine Geometrie XI: eine Minimum Aufgabe fur Legendres Tragheits Ellipsoid. Ber. Verh. Sachs. Akad. Wiss. Leipzig Math.-Phys. Kl. 70 (1918), 72–75.Google Scholar
5.Bonnesen, T. and Fenchel, W.. Theorie der Konvexen Korper (Springer, Berlin, 1934). English translation: Theory of Convex Bodies (BCS Associates, Moscow, Idaho, U.S.A., 1987).Google Scholar
6.Busemann, H.. A theorem on convex bodies of Brunn-Minkowski type. Proc. Nat. Acad. Sci. U.S.A. 35(1949), 27–31.CrossRefGoogle ScholarPubMed
7.Busemann, H.. Volume in terms of concurrent cross-sections. Pacific J. Math. 3 (1953), 1–12.CrossRefGoogle Scholar
8.Dupin, C.. Application de Geometrie et de Mechanique a la Marine, aux Points et Chaussees. (Bachelier, Paris, 1822).Google Scholar
9.Gardner, R. J.. Geometric Tomography (Cambridge University Press, Cambridge, 1995).Google Scholar
10.Lutwak, E.. On a conjectured projection inequality of Petty. Contemp. Math. 113 (1990), 171– 182.CrossRefGoogle Scholar
11.Lutwak, E.. selected affine isoperimetric inequalities. In Handbook of Convex Geometry (North-Holland, Amsterdam, 1993), 151–176.CrossRefGoogle Scholar
12.Milman, V. D. and Pajor, A.. Isotropic position and inertie ellipsoids and zonoids of the unit ball of a normed n-dimensional space. In Geometric Aspects of Functional Analysis (ed. Lindenstrauss, J. and Milman, V. D.), Lecture Notes Math. 1376 (Springer, 1989), 64–104.CrossRefGoogle Scholar
13.Petty, C. M.. Centroid surfaces. Pacific J. Math. 11 (1961), 1535–1547.CrossRefGoogle Scholar