  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.

Symplectic Geometry;Geometric Topology