Distance Functions, Curvature and Topology
Differential Geometry
2026-02-20 v1 Analysis of PDEs
Abstract
We discuss some properties of the distance functions on Riemannian manifolds and we relate their behavior to the geometry of the manifolds. This leads to alternative proofs of some "classical" theorems connecting curvature and topology.
Cite
@article{arxiv.2602.17629,
title = {Distance Functions, Curvature and Topology},
author = {Carlo Mantegazza and Francesca Oronzio},
journal= {arXiv preprint arXiv:2602.17629},
year = {2026}
}