Entropy of chord distribution of convex bodies

Xu, Wenxue

doi:10.1090/proc/14447

Entropy of chord distribution of convex bodies
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by Wenxue Xu

Proc. Amer. Math. Soc. 147 (2019), 3131-3141

DOI: https://doi.org/10.1090/proc/14447

Published electronically: March 15, 2019

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Abstract:

For a fixed convex body $K$ in $\mathbb R^n$, the chord distribution on the affine Grassmann manifold of lines is introduced and then the entropy of chord distribution is defined. Using the integral geometric method, we establish that the entropy of chord distribution of a convex body $K$ attains its minimum if and only if $K$ is a ball.

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