Upper and lower bounds on the filling radius

TL;DR

This paper establishes curvature-dependent bounds on the filling radius of closed Riemannian manifolds, explores the reach of Kuratowski embeddings, and discusses inequalities related to intermediate filling radii.

Contribution

It provides new curvature-dependent bounds for the filling radius and analyzes the reach of Kuratowski embeddings, extending understanding of geometric properties of Riemannian manifolds.

Findings

Lower bounds for filling radius based on curvature.

Upper bounds for manifolds with Riemannian submersion structures.

The reach of Kuratowski embedding images vanishes.

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.