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Abstract

Abstract. Let M be a closed three dimensional manifold with contact form λ so that ker λ is tight. In this paper we will present a first application of the filling method by pseudoholomorphic curves recently developed by the author. We will show that Legendrian knots L ⊂ M satisfying suitable assumptions admit a Reeb Chord, i.e. there is a trajectory x(t) of the Reeb vector field and T > 0 such that x(0), x(T ) ∈ L and x(0) = x(T ).