论文标题
Reeb流动着较小的接触量和较大的返回时间到全球部分
Reeb flows with small contact volume and large return time to a global section
论文作者
论文摘要
我们表明，任何尺寸的共同取向的封闭接触歧管至少五个承认接触形式，因此接触量很小，但是REEB流量允许截面的全局超浮雕与该特性的全局性超表面，该特性在高空表面的边界上最小的时期和高度曲线室内的第一个返回时间在下面有限制。该声明的直接结果是，任何封闭的歧管上的每个共同取向的接触结构都允许任意大型收缩比的接触表格。这概括了Abbondandolo等人的结果。在维度三到更高的维度中。证明主要结果是感应的，并使用了Abbondandolo等人的结果。在其基础步骤中以三个维度为单位的收缩比。证明中的基本结构依赖于较高维度的Giroux对应关系。
We show that any co-oriented closed contact manifold of dimension at least five admits a contact form such that the contact volume is arbitrarily small but the Reeb flow admits a global hypersurface of section with the property that the minimal period on the boundary of the hypersurface and the first return time in the interior of the hypersurface are bounded below. An immediate consequence of this statement is that every co-oriented contact structure on any closed manifold admits a contact form with arbitrarily large systolic ratio. This generalizes the result of Abbondandolo et al. in dimension three to higher dimensions. The proof the main result is inductive and uses the result of Abbondandolo et al. on large systolic ratio in dimension three in its basis step. The essential construction in the proof relies on the Giroux correspondence in higher dimensions.
