Mixed width-integrals of convex bodies |
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Authors: | Erwin Lutwak |
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Institution: | (1) Polytechnic Institute of New York, 11201 Brooklyn, New York, USA |
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Abstract: | The mixed width-integrals are defined and shown to have properties similar to those of the mixed volumes of Minkowski. An
inequality is established for the mixed width-integrals analogous to the Fenchel-Aleksandrov inequality for the mixed volumes.
An isoperimetric inequality (involving the mixed width-integrals) is presented which generalizes an inequality recently obtained
by Chakerian and Heil. Strengthened versions of this general inequality are obtained by introducing indexed mixed width-integrals.
This leads to an isoperimetric inequality similar to Busemann’s inequality involving concurrent cross-sections of convex bodies. |
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Keywords: | |
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