Isoperimetric constant

The article defines a scalar value (that is, a single real number) associated with a differential manifold. The scalar value may be dependent on certain additional structure with which the differential manifold is equipped

Definition

Given data

A closed orientable Riemannian manifold $M$ with $g$ being the Riemannian metric.

Definition part

The isoperimetric constant of $(M,g)$, denoted as $C_{s}(M,g)$ is defined as the infimum of the isoperimetric surfaces for every separating hypersurface.