A quantitative obstruction to collapsing surfaces

DOI10.1515/math-2019-0103zbMath1430.53044arXiv1604.06782OpenAlexW3101549537MaRDI QIDQ2278445

Mikhail G. Katz

Publication date: 5 December 2019

Published in: Open Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.06782

zbMATH Keywords

volumefilling radiuscurvaturediameterGromov-Hausdorff distancesystole

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (1)

Torus cannot collapse to a segment

Cites Work

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• Bi-Lipschitz approximation by finite-dimensional imbeddings
• Filling Riemannian manifolds
• Collapsing and pinching under a lower curvature bound
• Collapsing three-manifolds under a lower curvature bound.
• Small volume of balls, large volume entropy and the Margulis constant
• Differential geometry via infinitesimal displacements

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