Isoperimetric inequalities for finite perimeter sets under lower Ricci   curvature bounds
  We prove that the results regarding the Isoperimetric inequality and Cheeger constant formulated in terms of the Minkowski content, obtained by the authors in previous papers in the framework of essentially non-branching metric measure spaces verifying the local curvature dimension condition, also hold in the stronger formulation in terms of the perimeter. 
Fabio Cavalletti and Andrea Mondino
math.MG math.DG math.FA