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.

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