论文标题
截面和符号能力的磁盘状表面
Disk-like surfaces of section and symplectic capacities
论文作者
论文摘要
我们证明，在$ \ mathbb {r}^4 $中，动态凸域的圆柱能力与Reeb流动域的边界上的Reeb流的类似磁盘的全局表面的最小符号面积一致。此外，我们证明了$ \ mathbb {r}^4 $中所有凸形域的强viterbo猜想，它们足够$ c^3 $靠近圆球。这概括了Abbondolo-Bramham-Hryniewicz-Salomão的结果，为此类域建立了收缩不平等。
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 $C^3$ close to the round ball. This generalizes a result of Abbondandolo-Bramham-Hryniewicz-Salomão establishing a systolic inequality for such domains.
