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<p>In this paper, a strengthened Bonnesen inequality for closed convex plane curves will be given by strengthening its right-hand side into a nonnegative function <i>S</i>(<i>r</i>). For constant width curves, <i>S</i>(<i>r</i>) can be further written in a clearer form which can give us a strengthened Bonnesen-type inequality and an enhanced Gage inequality.</p>

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A strengthened form of the Bonnesen inequality

  • 期刊论文

  • 发表日期：

    2025年9月9日

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  • Shengliang Pan,
  • Yan Shu

摘要

In this paper, a strengthened Bonnesen inequality for closed convex plane curves will be given by strengthening its right-hand side into a nonnegative function S(r). For constant width curves, S(r) can be further written in a clearer form which can give us a strengthened Bonnesen-type inequality and an enhanced Gage inequality.