论文标题

平面曲线的一个属性,其凸壳覆盖给定的凸数字

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

论文作者

Nikonorov, Yu. G., Nikonorova, Yu. V.

论文摘要

在此注释中,我们证明了A. Akopyan和V. Vysotsky的以下猜想:如果平面曲线的凸壳$γ$涵盖平面凸$ K $,则$ \ opperatorname {length} {length}(γ)(γ)\ geq \ geq \ geq \ geq \ peratatornAme {per}(k) - \ permotatat -k)此外,研究了这种不平等的所有平等案例。

In this note, we prove the following conjecture by A. Akopyan and V. Vysotsky: If the convex hull of a planar curve $γ$ covers a planar convex figure $K$, then $\operatorname{length}(γ) \geq \operatorname{per} (K) - \operatorname{diam} (K)$. In addition, all cases of equality in this inequality are studied.

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