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Affine surface area and convex bodies of elliptic type

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Abstract

If a convex body K in \({\mathbb R}^n\) is contained in a convex body L of elliptic type (a curvature image), then it is known that the affine surface area of K is not larger than the affine surface area of L. We prove that the affine surface areas of K and L can only be equal if K = L.

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Acknowledgments

This work was initiated in March 2012 when I was a guest at the Rényi Institute of Mathematics in Budapest, supported by the ERC Advanced Research Grant No. 267165 (DISCONV). I thank Imre Bárány and the Rényi Institute for the great hospitality.

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  1. Mathematisches Institut, Albert-Ludwigs-Universität, 79104, Freiburg i. Br., Germany

    Rolf Schneider

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  1. Rolf Schneider
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Correspondence to Rolf Schneider.

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Schneider, R. Affine surface area and convex bodies of elliptic type. Period Math Hung 69, 120–125 (2014). https://doi.org/10.1007/s10998-014-0050-3

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  • DOI: https://doi.org/10.1007/s10998-014-0050-3

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