平面曲线的一种性质，其凸包覆盖了一个给定的凸图形

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

摘要

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

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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Elemente der Mathematik MATHEMATICS-

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