Title: Symplectic stability on manifolds with cylindrical ends,
Abstract: A famous result of Jurgen Moser states that a symplectic form on a compact
manifold cannot be deformed within its cohomology class to an inequivalent
symplectic form. It is well known that this does not hold in general for
noncompact symplectic manifolds. 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.