The paper is devoted to some extremal problems for convex curves and polygons in the Euclidean plane referring to the self Chebyshev radius. In particular, we determine the self Chebyshev radius for the boundary of an arbitrary triangle. Moreover, we derive the maximal possible perimeter for convex curves and boundaries of convex n-gons with a given self Chebyshev radius.

中文翻译：

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给定自切比雪夫半径的凸曲线的极值问题

论文针对自切比雪夫半径的欧几里得平面上的凸曲线和多边形的一些极值问题。特别是，我们确定任意三角形边界的自切比雪夫半径。此外，我们推导了具有给定自切比雪夫半径的凸曲线和凸n边的边界的最大可能周长。