Hofer’s symplectic energy and lagrangian intersections in contact geometry

Abstract

There is a version of Lagrangian intersection theory in contact geometry [2]. But it works well only with very restrictive contact manifolds. For example, it does not work well with overtwisted contact 3-manifolds. Here we show the following. If we have an estimate on Hamiltonian functions of contact flow, then we can apply the theory to a much wider class of contact manifolds.