Michor, Peter W.Mumford, David2010-02-122005Michor, Peter W., and David Bryant Mumford. 2005. Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Documenta Mathematica 10: 217-245.1431-06431431-0635http://nrs.harvard.edu/urn-3:HUL.InstRepos:3637112The L^2-metric or Fubini-Study metric on the non-linear Grassmannian of all submanifolds of type M in a Riemannian manifold (N, g) induces geodesic distance 0. We discuss another metric which involves the mean curvature and shows that its geodesic distance is a good topological metric. The vanishing phenomenon for the geodesic distance holds also for all diffeomorphism groups for the L^2-metric.en-USJournal Article2010-02-12