Width-integrals of convex bodies
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- by Erwin Lutwak
- Proc. Amer. Math. Soc. 53 (1975), 435-439
- DOI: https://doi.org/10.1090/S0002-9939-1975-0383254-5
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Abstract:
The width-integrals (Breitenintegrale) as introduced by Blaschke are examined. They are shown to satisfy a cyclic inequality similar to that satisfied by the cross-sectional measures (Quermassintegrale). Other similarities and inequalities between the width-integrals and the cross-sectional measures are shown to exist.References
- W. Blaschke, Vorlesungen über Integralgeometrie. I, II, Teubner, Leipzig, 1936, 1937; reprint, Chelsea, New York, 1949.
T. Bonnesen and W. Fenchel, Theorie der konvexen Körpern, Springer, Berlin, 1934; reprint, Chelsea, New York, 1948.
- Branko Grünbaum, Measures of symmetry for convex sets, Proc. Sympos. Pure Math., Vol. VII, Amer. Math. Soc., Providence, R.I., 1963, pp. 233–270. MR 0156259
- H. Guggenheimer, Polar reciprocal convex bodies, Israel J. Math. 14 (1973), 309–316. MR 320888, DOI 10.1007/BF02764893
- H. Hadwiger, Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957 (German). MR 0102775 G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, London, 1934.
- Erwin Lutwak, Dual mixed volumes, Pacific J. Math. 58 (1975), no. 2, 531–538. MR 380631
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 435-439
- MSC: Primary 52A40
- DOI: https://doi.org/10.1090/S0002-9939-1975-0383254-5
- MathSciNet review: 0383254