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.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/3050