, Volume 19, Issue 6, pp 1688-1692
Date: 12 Feb 2010

Systolic Inequalities and Minimal Hypersurfaces

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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.