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arXiv · 2004.01505

Tori Can't Collapse to an Interval

Sergio Zamora
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Abstract

Here we prove that under a lower sectional curvature bound, a sequence of Riemannian manifolds diffeomorphic to the standard $m$-dimensional torus cannot converge in the Gromov--Hausdorff sense to a closed interval. The proof is done by contradiction by analyzing suitable covers of a contradicting sequence, obtained from the Burago--Gromov--Perelman generalization of the Yamaguchi fibration theorem.

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Sergio Zamora. 2020-03-30. Tori Can't Collapse to an Interval. https://doi.org/10.3934/era.2021005

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