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math.MG2023
The extreme polygons for the self Chebyshev radius of the boundary
Evgenii V. Nikitenko, Yurii G. Nikonorov
The paper is devoted to some extremal problems for convex polygons on the Euclidean plane, related to the concept of self Chebyshev radius for the polygon boundary. We consider a g…
math.MG2020★ 5 cited
Extreme problems for convex curves with given relative Chebyshev radius
Vitor Balestro, Horst Martini, Yurii Nikonorov +1
The paper is devoted to some extremal problems for convex curves and polygons in the Euclidean plane referring to the relative Chebyshev radius. In particular, we determine the rel…
math.MG2020
One property of a planar curve whose convex hull covers a given convex figure
Yu. G. Nikonorov, Yu. V. Nikonorova
In this note, we prove the following conjecture by A. Akopyan and V. Vysotsky: If the convex hull of a planar curve covers a planar convex figure , then $\operatorname{lengt…