Isoperimetric constant

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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.