  In the setting of symplectic manifolds which are convex at infinity, we use a
version of the Aleksandrov maximum principle to derive uniform estimates for
Floer solutions that are valid for a wider class of Hamiltonians and almost
complex structures than is usually considered. This allows us to extend the
class of Hamiltonians which one can use in the direct limit when constructing
symplectic homology. As an application, we detect elements of infinite order in
the symplectic mapping class group of a Liouville domain, and obtain existence
results for translated points.
