  The fundamental properties of $J$-holomorphic maps depend on two
inequalities: The gradient inequality gives a pointwise bound on the
differential of a $J$-holomorphic map in terms of its energy. The cylinder
inequality stipulates and quantifies the exponential decay of energy along
cylinders of small total energy. We show these inequalities hold uniformly if
the geometry of the target symplectic manifold and Lagrangian boundary
condition is appropriately bounded.
