Systolic inequalities and minimal hypersurfaces

2009/03/31 by Larry Guth, Guth, Larry · 2 citations
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.0903.5299

Abstract

We give a short proof of the systolic inequality for the n-dimensional torus. The proof uses minimal hypersurfaces. It is based on the Schoen-Yau proof that an n-dimensional torus admits no metric of positive scalar curvature.

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• Morse Spectra, Homology Measures and Parametric Packing Problems
• Covering instability for the existence of positive scalar curvature metrics
• Hyperellipticity and Klein bottle companionship in systolic geometry
• Cohomological dimension, self-linking, and systolic geometry

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