Submanifold averaging in riemannian and symplectic geometry

Abstract

We give a construction to obtain canonically an “isotropic average” of given $C^1$-close isotropic submanifolds of a symplectic manifold. To do so we use an improvement of Weinstein's submanifold averaging theorem (obtained in collaboration with H. Karcher) and apply “Moser's trick”. We also present an application to Hamiltonian group actions.