2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96713We 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.New title (old title: "Averaging of isotropic submanifolds"), paper re-written and expanded. Added: improvement of Weinstein's averaging theorem (Section 2), application to Hamiltonian actions (Section 9). Statement of main theorem improved. Introduction re-writtenDifferential GeometrySymplectic Geometry53C55; 53D12text