One property of a planar curve whose convex hull covers a given convex figure

IF 0.1 Q4 MATHEMATICS Elemente der Mathematik Pub Date : 2020-07-01 DOI:10.4171/EM/458
Y. Nikonorov, Y. Nikonorova
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引用次数: 1

Abstract

In this note, we prove the following conjecture by A. Akopyan and V. Vysotsky: If the convex hull of a planar curve $\gamma$ covers a planar convex figure $K$, then $\operatorname{length}(\gamma) \geq \operatorname{per} (K) - \operatorname{diam} (K)$. In addition, all cases of equality in this inequality are studied.
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平面曲线的一种性质,其凸包覆盖了一个给定的凸图形
在本文中,我们证明了A.Akopyan和V.Vysotsky的以下猜想:如果平面曲线$\gamma$的凸包覆盖平面凸图$K$,则$\operatorname{length}(\gamma)\geq\operatorname{per}(K)-\operatorname{diam}(K)$。此外,还研究了这种不平等中的所有平等情况。
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