Linear bounds for constants in Gromov's systolic inequality and related results

DOI10.2140/gt.2022.26.3123OpenAlexW4318897336MaRDI QIDQ2683198

Alexander Nabutovsky

Publication date: 3 February 2023

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.12225

zbMATH Keywords

isoperimetric inequalitysystoleHausdorff contentsystolic inequalitygeometry of metric spacesshortest periodic geodesic

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) Lipschitz and coarse geometry of metric spaces (51F30)

Cites Work

• Volumes of balls in large Riemannian manifolds
• Uryson width and volume
• The filling radius of two-point homogeneous spaces
• Filling Riemannian manifolds
• Filling metric spaces
• Systolic inequalities and minimal hypersurfaces
• Volumes of balls in Riemannian manifolds and Uryson width
• The conservation property of the heat equation on riemannian manifolds
• A short proof of Gromov's filling inequality

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