## 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
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## 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