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arXiv · 2506.00763

Torus covers with controlled volume and diameter

Sergio Zamora
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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.

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Sergio Zamora. 2025-06-01. Torus covers with controlled volume and diameter. https://arxiv.org/abs/2506.00763

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