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- W3202198105 abstract "In this note, we prove the following inequality for the norm of a convex body $K$ in $mathbb{R}^n$, $ngeq 2$: $N(K) leq frac{pi^{frac{n-1}{2}}}{2 Gamma left(frac{n+1}{2}right)}cdot operatorname{length} (gamma) + frac{pi^{frac{n}{2}-1}}{Gamma left(frac{n}{2}right)} cdot operatorname{diam}(K)$, where $operatorname{diam}(K)$ is the diameter of $K$, $gamma$ is any curve in $mathbb{R}^n$ whose convex hull covers $K$, and $Gamma$ is the gamma function. If in addition $K$ has constant width $Theta$, then we get the inequality $operatorname{length} (gamma) geq frac{2(pi-1)Gamma left(frac{n+1}{2}right)}{sqrt{pi},Gamma left(frac{n}{2}right)}cdot Theta geq 2(pi-1) cdot sqrt{frac{n-1}{2pi}}cdot Theta$. In addition, we pose several unsolved problems." @default.
- W3202198105 created "2021-10-11" @default.
- W3202198105 creator A5047975487 @default.
- W3202198105 date "2021-09-27" @default.
- W3202198105 modified "2023-09-27" @default.
- W3202198105 title "Properties of a curve whose convex hull covers a given convex body." @default.
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