We obtain several results for (iterated) planar contact manifolds in higher dimensions: (1) Iterated planar contact manifolds are not weakly symplectically semi-fillable. This generalizes a 3-dimensional result of Etnyre to a higher-dimensional setting. (2) They do not arise as nonseparating weak contact-type hypersurfaces in closed symplectic manifolds. This generalizes a result by Albers-Bramham-Wendl. (3) They satisfy the Weinstein conjecture, i.e. every contact form admits a closed Reeb orbit. This is proved by an alternative approach as that of [Acu], and is a higher-dimensional generalization of a result of Abbas-Cieliebak-Hofer. The results follow as applications from a suitable symplectic handle attachment, which bears some independent interest.

中文翻译：

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高维接触流形中的平面性

我们在更高维度上获得了（迭代的）平面接触流形的几个结果：（1）迭代的平面接触流形不是弱辛半可填充的。这将 Etnyre 的 3 维结果推广到更高维的设置。(2) 它们不会作为闭合辛流形中的非分离弱接触型超曲面出现。这概括了 Albers-Bramham-Wendl 的结果。(3)它们满足韦恩斯坦猜想，即每个接触形式都承认一个闭合的Reeb轨道。这是由 [Acu] 的替代方法证明的，并且是 Abbas-Cieliebak-Hofer 结果的高维概括。结果是来自合适的辛手柄附件的应用程序，它具有一些独立的兴趣。