Torus covers with controlled volume and diameter
Sergio Zamora

TL;DR
This paper proves that under certain curvature and diameter constraints, a torus has a finite covering with controlled volume and diameter, partially addressing a previous result with an unresolved gap.
Contribution
It provides a new proof of a covering space property for tori under curvature and diameter bounds, addressing gaps in prior work.
Findings
Existence of finite coverings with bounded volume and diameter
Partial recovery of a previous theorem by Kloeckner and Sabourau
Addresses gaps in earlier proofs regarding torus coverings
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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Taxonomy
TopicsTribology and Lubrication Engineering · Tunneling and Rock Mechanics
