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Geometric and Functional Analysis

, Volume 19, Issue 6, pp 1688–1692 | Cite as

Systolic Inequalities and Minimal Hypersurfaces

  • Larry Guth
Article

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

Systole minimal surface scalar curvature 

2010 Mathematics Subject Classification

53C23 

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References

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Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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