Reeb dynamics, holomorphic discs, and the 4-ball

This is joint work with Hansjörg Geiges. Extending our work on Cerf's theorem we apply our moduli-theoretic version of Eliashberg-Hofer's filling-with-holomorphic-discs method to symplectic manifolds with cylindrical ends. Is the tight 3-sphere one of its positive ends we obtain existence results for contractible closed Reeb orbits, filling obstructions, and non-existence results for Liouville cobordisms.