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The mixed area of a convex body and its polar reciprocal

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Abstract

Half the vector sum of a convex body and its polar reciprocal with respect to a unit sphereE containsE. A consequence of this is: The mixed area of a plane convex body and its polar reciprocal with respect toE is minimized by circles concentric withE.

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Reference

  1. Bonnesen, T. and Fenchel, W., 1934,Theorie der konvexen Körper, Berlin.

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Authors and Affiliations

  1. Oregon State University, Corvallis, Oregon

    Wm. J. Firey

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  1. Wm. J. Firey
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Additional information

This work was supported in part by a grant from the National Science Foundation, NSF-G 19838. The author is indebted to the referee for fruitful comments.

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Firey, W.J. The mixed area of a convex body and its polar reciprocal. Israel J. Math. 1, 201–202 (1963). https://doi.org/10.1007/BF02759718

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  • DOI: https://doi.org/10.1007/BF02759718

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