Systolic Inequalities and Minimal Hypersurfaces
- First Online:
- Cite this article as:
- Guth, L. Geom. Funct. Anal. (2010) 19: 1688. doi:10.1007/s00039-010-0052-0
- 144 Downloads
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.