Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds

Abstract This paper studies sharp and rigid isoperimetric comparison theorems asymptotic properties for small large volumes on N -dimensional $$\textrm{RCD}(K,N)$$ RCD ( K , N ) spaces $$(X,\textsf {d},\mathscr {H}^N)$$ X d H . Moreover, we obtain almost regularity formulated in terms of the profile enhanced consequences at level several functional inequalities. Most our statements seem to be new even classical setting smooth, non compact manifolds with lower Ricci curvature bounds. The synthetic theory plays a key role via compactness stability arguments.