Sharp systolic inequalities for $3$-manifolds with boundary
Differential Geometry
2020-11-03 v4
Abstract
We prove some sharp systolic inequalities for compact -manifolds with boundary. They relate the (relative) homological systoles of the manifold to its scalar curvature and mean curvature of the boundary. In the equality case, the universal cover of the manifold is isometric to a cylinder over a disk of nonnegative constant curvature.
Keywords
Cite
@article{arxiv.1912.08798,
title = {Sharp systolic inequalities for $3$-manifolds with boundary},
author = {Eduardo Longa},
journal= {arXiv preprint arXiv:1912.08798},
year = {2020}
}
Comments
Final version (8 pages). To appear in The Journal of Geometric Analysis