Metaphors in systolic geometry

Abstract

This is an expository essay about systolic geometry. It describes a central theorem in the subject and why the proof is difficult. Then it discusses different metaphors which suggest ways to approach the problem. The metaphors connect the systolic inequality to minimal surfaces, topological dimension, scalar curvature, and hyperbolic geometry.

28 pages, 1 figure.

References in corpus (1)

• Diastolic and isoperimetric inequalities on surfaces

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• Volumes of balls in Riemannian manifolds and Uryson width