Surveys in Differential Geometry
Volume 21 (2016)
Constant mean curvature surfaces
Pages: 179 – 287
In this article we survey recent developments in the theory of constant mean curvature surfaces in homogeneous 3-manifolds, as well as some related aspects on existence and descriptive results for $H$-laminations and CMC foliations of Riemannian $n$-manifolds.
minimal surface, constant mean curvature, minimal lamination, $H$-lamination, CMC foliation, locally simply connected, Jacobi function, stability, index of stability, Shiffman function, curvature estimates, parking garage structure, flocal picture on the scale of topology, Willmore energy
2010 Mathematics Subject Classification
Primary 53A10. Secondary 49Q05, 53C42.