Abstract
We give a curvature dependent lower bound for the filling radius of all closed Riemannian manifolds as well as an upper one for manifolds which are the total space of a Riemannian submersion. The latter applies also to the case of submetries. We also see that the reach (in the sense of Federer) of the image of the Kuratowski embedding vanishes, and we finish by giving some inequalities involving the k-intermediate filling radius.
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