English

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.

Keywords

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}
}