Communications in Analysis and Geometry
Volume 18 (2010)
Surfaces with maximal constant mean curvature
Pages: 627 – 647
In this note we consider asymptotically flat manifolds withnon-negative scalar curvature and an inner boundary whichis an outermost minimal surface. We show that there existsan upper bound for the mean curvature of a constant meancurvature (CMC) surface homologous to a subset of theinterior boundary components. This bound allows us to finda maximizer for the CMC of a surface homologous to theinner boundary.
With this maximizer at hand, we can construct an increasingfamily of sets with boundaries of increasing CMC. Weinterpret this family as a weak version of a CMC foliation.