We prove that the cylindrical capacity of a dynamically convex domain in \({\mathbb{R}}^{4}\) agrees with the least symplectic area of a disk-like global surface of section of the Reeb flow on the boundary of the domain. Moreover, we prove the strong Viterbo conjecture for all convex domains in \({\mathbb{R}}^{4}\) which are sufficiently C³ close to the round ball. This generalizes a result of Abbondandolo-Bramham-Hryniewicz-Salomão establishing a systolic inequality for such domains.

中文翻译：

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盘状截面和辛容量

我们证明 \({\mathbb{R}}^{4}\) 中动态凸域的柱容量与 Reeb 流边界上的盘状全局表面的最小辛面积一致域。此外，我们证明了 \({\mathbb{R}}^{4}\) 中所有 C ³ 足够接近圆球的凸域的强维特博猜想。这概括了 Abbondandolo-Bramham-Hryniewicz-Salomão 为这些域建立收缩不等式的结果。