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<p>This article provides a survey of relatively recent results on several extremal problems in&#xa0;geometry.Some of the problems under consideration concern estimating areas and perimeters of planar figures,some concern the study of the self Chebyshev radius of the boundary of convex figures, and some are directly connected with the geometry of Minkowski planes.Moreover, we discuss problems related to the properties of curves in multidimensionalEuclidean spaces and to the geodesic diameter of spheres endowed with intrinsic metrics and involutive isometries.For certain problems, complete solutions are presented, while for others only hints toward solutions are provided.In addition, a number of related, still unsolved problems are considered.</p>

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Some Extremal Geometrical Problems

  • 期刊论文

  • 发表日期：

    2025年9月30日

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  • Yu. G. Nikonorov

摘要

This article provides a survey of relatively recent results on several extremal problems in geometry.Some of the problems under consideration concern estimating areas and perimeters of planar figures,some concern the study of the self Chebyshev radius of the boundary of convex figures, and some are directly connected with the geometry of Minkowski planes.Moreover, we discuss problems related to the properties of curves in multidimensionalEuclidean spaces and to the geodesic diameter of spheres endowed with intrinsic metrics and involutive isometries.For certain problems, complete solutions are presented, while for others only hints toward solutions are provided.In addition, a number of related, still unsolved problems are considered.