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

Autor:	Nikonorov, Yu. G., Nikonorova, Yu. V.
Rok vydání:	2020
Předmět:	Mathematics - Metric Geometry 52A10 52A40 53A04
Druh dokumentu:	Working Paper
DOI:	10.4171/EM/458
Popis:	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. Comment: 10 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2007.00612 Zobrazit plný text záznamu View this record from Arxiv