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<p>An upper estimate of the new curvature entropy is provided, via the integral inequality of a concave function. For two origin-symmetric convex bodies in ℝ<sup><i>n</i></sup>, this bound is sharper than the log-Minkowski inequality of curvature entropy. As its application, a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.</p>

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Notes on the log-Minkowski inequality of curvature entropy

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Deyi Li,
  • Lei Ma,
  • Chunna Zeng

摘要

An upper estimate of the new curvature entropy is provided, via the integral inequality of a concave function. For two origin-symmetric convex bodies in ℝn, this bound is sharper than the log-Minkowski inequality of curvature entropy. As its application, a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.