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<p>Using optimal transport, we prove a sharp, dimension-free isoperimetric inequality involving volume entropy for metric measure spaces with non-negative Ricci curvature in the sense of Lott-Sturm-Villani. Furthermore, we prove rigidity for RCD(0, ∞) spaces via Bakry-Émery’s Γ<sub>2</sub>-calculus. These results are new even for Euclidean spaces equipped with log-concave densities and are of interest in both probability theory and geometry.</p>

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Sharp and rigid isoperimetric inequalities in metric measure spaces with non-negative Ricci curvature

  • 期刊论文

  • 发表日期：

    2026年7月1日

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  • Bang-Xian Han

摘要

Using optimal transport, we prove a sharp, dimension-free isoperimetric inequality involving volume entropy for metric measure spaces with non-negative Ricci curvature in the sense of Lott-Sturm-Villani. Furthermore, we prove rigidity for RCD(0, ∞) spaces via Bakry-Émery’s Γ2-calculus. These results are new even for Euclidean spaces equipped with log-concave densities and are of interest in both probability theory and geometry.