Constant mean curvature surfaces

William H. Meeks III; Joaquin Perez; Giuseppe Tinaglia

doi:10.4310/SDG.2016.v21.n1.a6

Constant mean curvature surfaces

William H. Meeks III, Joaquin Perez, Giuseppe Tinaglia

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Abstract

In this article we survey recent developments in the theory of constant mean cur- vature surfaces in homogeneous 3-manifolds, as well as some related aspects on ex- istence and descriptive results for H -laminations and CMC foliations of Riemannian n -manifolds. Mathematics Subject Classi cation: Primary 53A10, Secondary 49Q05, 53C42. Key words and phrases: Minimal surface, constant mean curvature, minimal lamina- tion, H -lamination, CMC foliation, locally simply connected, Jacobi function, stabil- ity, index of stability, Shi man function, curvature estimates, parking garage structure, local picture on the scale of topology, Willmore energy.

Original language	English
Pages (from-to)	179-287
Number of pages	9
Journal	Surveys in Differential Geometry
DOIs	https://doi.org/10.4310/SDG.2016.v21.n1.a6
Publication status	Published - 7 Jun 2016

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Constant mean curvature surfaces_WEEKS_AcceptedJune2016_Green AAMAccepted author manuscript, 2.88 MB

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title = "Constant mean curvature surfaces",

abstract = "In this article we survey recent developments in the theory of constant mean cur- vature surfaces in homogeneous 3-manifolds, as well as some related aspects on ex- istence and descriptive results for H -laminations and CMC foliations of Riemannian n -manifolds. Mathematics Subject Classi cation: Primary 53A10, Secondary 49Q05, 53C42. Key words and phrases: Minimal surface, constant mean curvature, minimal lamina- tion, H -lamination, CMC foliation, locally simply connected, Jacobi function, stabil- ity, index of stability, Shi man function, curvature estimates, parking garage structure, local picture on the scale of topology, Willmore energy.",

author = "{H. Meeks III}, William and Joaquin Perez and Giuseppe Tinaglia",

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AU - Perez, Joaquin

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AB - In this article we survey recent developments in the theory of constant mean cur- vature surfaces in homogeneous 3-manifolds, as well as some related aspects on ex- istence and descriptive results for H -laminations and CMC foliations of Riemannian n -manifolds. Mathematics Subject Classi cation: Primary 53A10, Secondary 49Q05, 53C42. Key words and phrases: Minimal surface, constant mean curvature, minimal lamina- tion, H -lamination, CMC foliation, locally simply connected, Jacobi function, stabil- ity, index of stability, Shi man function, curvature estimates, parking garage structure, local picture on the scale of topology, Willmore energy.

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JO - Surveys in Differential Geometry

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Constant mean curvature surfaces

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