Submanifold averaging in Riemannian and symplectic geometry
We give a canonical construction of an “isotropic average” of given -close isotropic submanifolds of a symplectic manifold. For this purpose we use an improvement (obtained in collaboration with H. Karcher) of Weinstein’s submanifold averaging theorem and apply “Moser’s trick”. We also present an application to Hamiltonian group actions.