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The Zaporozhets-Tarasov Conjecture on Mean Distances
For a convex body $K \subset \mathbb R^d$ let $Δ(K)$ be the expected distance between two independent uniform points of $K$, and let $θ(K)$ be the corresponding expectation for normalized surface measure on $\partial K$. The Zaporozhets-Tarasov conjecture asserts $Δ(K) \le θ(K)$. We prove this conje
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