  Consider a Hamiltonian torus action on a connected symplectic manifold M for
which the associated moment map Phi is proper in some sense. Let Q be a closed
submanifold of M. We show that under certain local conditions on Q one has
Phi(Q)=Phi(M). We apply this result in the special case that Q arises as the
fixed point set of some involution on M which is not necessarily
antisymplectic.
