  We find the minimax rate of convergence in Hausdorff distance for estimating
a manifold M of dimension d embedded in R^D given a noisy sample from the
manifold. We assume that the manifold satisfies a smoothness condition and that
the noise distribution has compact support. We show that the optimal rate of
convergence is n^{-2/(2+d)}. Thus, the minimax rate depends only on the
dimension of the manifold, not on the dimension of the space in which M is
embedded.
