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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Width-integrals of convex bodies


Author: Erwin Lutwak
Journal: Proc. Amer. Math. Soc. 53 (1975), 435-439
MSC: Primary 52A40
MathSciNet review: 0383254
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] W. Blaschke, Vorlesungen über Integralgeometrie. I, II, Teubner, Leipzig, 1936, 1937; reprint, Chelsea, New York, 1949.
  • [2] T. Bonnesen and W. Fenchel, Theorie der konvexen Körpern, Springer, Berlin, 1934; reprint, Chelsea, New York, 1948.
  • [3] 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 (27 #6187)
  • [4] H. Guggenheimer, Polar reciprocal convex bodies, Israel J. Math. 14 (1973), 309–316. MR 0320888 (47 #9421)
  • [5] H. Hadwiger, Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957 (German). MR 0102775 (21 #1561)
  • [6] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, London, 1934.
  • [7] Erwin Lutwak, Dual mixed volumes, Pacific J. Math. 58 (1975), no. 2, 531–538. MR 0380631 (52 #1528)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0383254-5
PII: S 0002-9939(1975)0383254-5
Keywords: Cross-sectional measures, Hölder's Inequality, Minkowski's Inequality, polar body, support function, width, width-integrals
Article copyright: © Copyright 1975 American Mathematical Society