Finite energy cylinders of small area

Abstract

\widetilde{J} -holomorphic cylinders in \mathbb{R}\times M , where M is a contact manifold are investigated. It is shown that a sufficiently long cylinder having small area is close to a constant map, if its center action vanishes. If its center action is positive, it is close to a cylinder over a periodic orbit of the Reeb vector field, and has a well-determined shape. A compactness result is deduced, which is useful in symplectic field theory.