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<p>We introduce a way of measuring nonconvexity of a metric space. We apply it to define a broad generalization and refinement of the classical curvature of a curve. We also use it to introduce a natural new notion of a fractal set.</p>

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Holes, nonconvexity, and curvature in metric spaces

  • 期刊论文

  • 发表日期：

    2026年3月26日

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  • William Geller,
  • Michał Misiurewicz

摘要

We introduce a way of measuring nonconvexity of a metric space. We apply it to define a broad generalization and refinement of the classical curvature of a curve. We also use it to introduce a natural new notion of a fractal set.