Linear isoperimetric inequality for homogeneous Hadamard manifolds

TL;DR

This paper extends the known linear isoperimetric inequality from symmetric spaces of non-positive curvature to a broader class of homogeneous Hadamard manifolds, enhancing understanding of geometric filling properties.

Contribution

The authors generalize the linear isoperimetric inequality to homogeneous Hadamard manifolds, broadening the scope beyond symmetric spaces.

Findings

Established linear isoperimetric inequality for homogeneous Hadamard manifolds

Extended known results from symmetric spaces to more general homogeneous spaces

Provided new insights into geometric filling properties of non-positively curved manifolds

Abstract

It is well known that simply connected symmetric spaces of non-positive sectional curvature admit a linear isoperimetric filling inequality for cycles of dimension greater than or equal to the rank of the space. In this note we extend that result to homogeneous Hadamard manifolds.