Geometric and Functional Analysis

, Volume 19, Issue 6, pp 1688–1692

Systolic Inequalities and Minimal Hypersurfaces

Article

DOI: 10.1007/s00039-010-0052-0

Cite this article as:
Guth, L. Geom. Funct. Anal. (2010) 19: 1688. doi:10.1007/s00039-010-0052-0

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.

Keywords and phrases

Systoleminimal surfacescalar curvature

2010 Mathematics Subject Classification

53C23

Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada