Uniform waist inequalities in codimension two for manifolds with Kazhdan fundamental group

TL;DR

This paper proves that manifolds with Kazhdan fundamental groups have uniform waist inequalities in codimension two, extending known results from codimension one to higher codimension for their finite covers.

Contribution

It establishes a new uniform waist inequality in codimension two for finite covers of manifolds with Kazhdan fundamental groups, expanding the scope of geometric inequalities.

Findings

Finite covers of M satisfy a uniform waist inequality in codimension two.

Extension of Cheeger inequality results from codimension one to codimension two.

Supports the geometric rigidity of manifolds with Kazhdan fundamental groups.

Abstract

Let M be a closed Riemannian manifold with Kazhdan fundamental group. It is well known that the Cheeger inequality yields a uniform waist inequality in codimension one for the finite covers of M. We show that the finite covers of M also satisfy a uniform waist inequality in codimension two.