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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Volume of mixed bodies
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by Erwin Lutwak
Trans. Amer. Math. Soc. 294 (1986), 487-500
DOI: https://doi.org/10.1090/S0002-9947-1986-0825717-3

Abstract:

By using inequalities obtained for the volume of mixed bodies and the Petty Projection Inequality, (sharp) isoperimetric inequalities are derived for the projection measures (Quermassintegrale) of a convex body. These projection measure inequalities, which involve mixed projection bodies (zonoids), are shown to be strengthened versions of the classical inequalities between the projection measures of a convex body. The inequality obtained for the volume of mixed bodies is also used to derive a form of the Brunn-Minkowski inequality involving mixed bodies. As an application, inequalities are given between the projection measures of convex bodies and the mixed projection integrals of the bodies.
References
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Bibliographic Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 294 (1986), 487-500
  • MSC: Primary 52A40; Secondary 52A22
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0825717-3
  • MathSciNet review: 825717