Torus cannot collapse to a segment

DOI10.1007/s00022-020-0525-8zbMath1437.53029arXiv2002.07523OpenAlexW3104321287MaRDI QIDQ2309611

Mikhail G. Katz

Publication date: 1 April 2020

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.07523

zbMATH Keywords

torusKlein bottlecollapsing Riemannian manifolds

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (3)

The Gromov-Hausdorff distance between spheres ⋮ Tori can't collapse to an interval ⋮ New invariants of Gromov-Hausdorff limits of Riemannian surfaces with curvature bounded below

Uses Software

• MathOverflow

Cites Work

• Unnamed Item
• The filling radius of two-point homogeneous spaces
• Collapsing and pinching under a lower curvature bound
• Shortening curves on surfaces
• Collapsing three-manifolds under a lower curvature bound.
• A quantitative obstruction to collapsing surfaces
• Differential geometry via infinitesimal displacements
• Filling Radius and Short Closed Geodesics of the $2$-Sphere
• Non-standard analysis

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