Torus covers with controlled volume and diameter
Differential Geometry
2025-08-12 v2 Metric Geometry
Abstract
We show that under a lower Ricci curvature bound and an upper diameter bound, a torus admits a finite-sheeted covering space with volume bounded from below and diameter bounded from above. This partially recovers a result of Kloeckner and Sabourau, whose original proof contains a serious gap that currently lacks a resolution.
Cite
@article{arxiv.2506.00763,
title = {Torus covers with controlled volume and diameter},
author = {Sergio Zamora},
journal= {arXiv preprint arXiv:2506.00763},
year = {2025}
}
Comments
Added Example 35