# Isoperimetric constant

From Diffgeom

*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 with being the Riemannian metric.

### Definition part

The isoperimetric constant of , denoted as is defined as the infimum of the isoperimetric surfaces for every separating hypersurface.