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<p>In this paper, we prove the Wulff–Gage isoperimetric inequality for origin-symmetric convex bodies and the uniqueness of the log-Minkowski problem in ℝ<sup>2</sup>. Then we give a new proof of the log-Minkowski inequality of curvature entropy for origin-symmetric convex bodies with <i>C</i><sup>2</sup> boundaries.</p>

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Notes on the Wulff–Gage Isoperimetric Inequality

  • 期刊论文

  • 发表日期：

    2025年9月15日

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  • Lei Ma,
  • Chunna Zeng

摘要

In this paper, we prove the Wulff–Gage isoperimetric inequality for origin-symmetric convex bodies and the uniqueness of the log-Minkowski problem in ℝ2. Then we give a new proof of the log-Minkowski inequality of curvature entropy for origin-symmetric convex bodies with C2 boundaries.