  The present paper describes a way to relate Martin boundaries on spaces of
varying topology. This enables us to approach some detailed inductive analysis
of the eigenfunctions of conformal Laplacians on minimal hypersurfaces near
their singularities. This can directly be used resp. translated to understand
the way how such minimal hypersurfaces inherit positive scalar curvature from
their ambience resp. how to smooth singular minimal hypersurfaces to regular
hypersurfaces with positive mean curvature.
