Symplectic manifolds, $L^p$-cohomology and $q$-parabolicity

Abstract

Let $(M,\omega ,J,g)$ be a non-compact almost Kähler manifold. In this paper we provide various criteria that assure that ${\omega }^k$ induces a non trivial class in the reduced $L^p$ maximal/minimal cohomology of $(M,g)$. Furthermore in the last part we explore some topological applications of our results.

Final version. To appear on Differential Geometry and its Applications