Symplectic Stability on Manifolds with Cylindrical Ends

The notion of Eliashberg–Gromov convex ends provides a natural restricted setting for the study of analogs of Moser’s symplectic stability result in the noncompact case, and this has been significantly developed in work of Cieliebak–Eliashberg. Retaining the end structure on the underlying smooth manifold, but dropping the convexity and completeness assumptions on the symplectic forms at infinity, we show that symplectic stability holds under a natural growth condition on the path of symplectic forms. The result can be straightforwardly applied as we show through explicit examples.