Extreme problems for convex curves with given relative Chebyshev radius

Vitor Balestro, Horst Martini, Yurii Nikonorov, Yulia Nikonorova

Published 2020-10-13Version 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 relative Chebyshev radius for an arbitrary triangle. Moreover, we derive the maximal possible perimeter for convex curves and convex n-gons of a given relative Chebyshev radius.