Some Remarks on Uniformly Regular Riemannian Manifolds

TL;DR

This paper demonstrates that the class of closed uniformly regular Riemannian manifolds is equivalent to the class of complete manifolds with bounded geometry, clarifying their relationship in geometric analysis.

Contribution

It establishes the equivalence between uniformly regular and bounded geometry Riemannian manifolds, providing a clearer understanding of their geometric properties.

Findings

Equivalence between uniformly regular and bounded geometry manifolds.

Characterization of closed uniformly regular Riemannian manifolds.

Implications for geometric analysis and manifold classification.

Abstract

We establish the equivalence between the family of closed uniformly regular Riemannian manifolds and the class of complete manifolds with bounded geometry.