Surveys in Differential Geometry

Volume 21 (2016)

Constant mean curvature surfaces

Pages: 179 – 287

DOI: http://dx.doi.org/10.4310/SDG.2016.v21.n1.a6

Authors

William H. Meeks, III (Department of Mathematics, University of Massachusetts, Amherst, Mass., U.S.A.)

Joaquín Pérez (Department of Geometry and Topology and Institute of Mathematics (IEMath-GR), University of Granada, Spain)

Giuseppe Tinaglia (Department of Mathematics, Kings College London, United Kingdom)

Abstract

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.

Keywords

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.

Full Text (PDF format)

Published 7 June 2016