  A weighted nonlinear flag is a nested set of closed submanifolds, each
submanifold endowed with a volume density. We study the geometry of Frechet
manifolds of weighted nonlinear flags, in this way generalizing the weighted
nonlinear Grassmannians. When the ambient manifold is symplectic, we use these
nonlinear flags to describe a class of coadjoint orbits of the group of
Hamiltonian diffeomorphisms, orbits that consist of weighted isotropic
nonlinear flags.
