  Scalar curvature constraints can be studied by means of splitting procedures.
The success of this strategy depends on the control we can get on its splitting
factors. We introduce canonical so-called minimal splitting factors. They have
positive scalar curvature while other properties strongly resemble those of
area minimizing hypersurfaces. This includes the presence of Poincare, Sobolev
and isoperimetric inequalities and the fact that singular points admit tangent
cones but now with positive scalar curvature.
