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

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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