Closely related with the dynamics of General Relativity in the Maximal and Constant Mean Curvature gauge is the problem of understanding the relation between scalar curvature, isoperimetry and integral (Lp) curvature in dimension three. We will discuss the proof a theorem saying that a positive lower bound on the scalar curvature, and the Lp (p>3/2) norm of the Ricci tensor control the isoperimetric constant and thus prevent isoperimetric collapse. The proof is based on a technique that uses size relations of stable minimal tubes to understand (and rule out) collapsed regions.