3.4 Prescribed mean curvature
The above results concerning the existence of CMC foliations are based on the assumption of the
existence of one CMC hypersurface. There are ways to circumvent this condition. By proving the existence
of a suitable prescribed mean curvature (PMC) foliation, it is sometimes possible to construct barriers that
imply the existence of one CMC hypersurface; see Section 3.6 of [69] and references cited therein for more
details.