Constant mean curvature surfaces
William H. Meeks III, Joaquin Perez, Giuseppe Tinaglia
TL;DR
This paper surveys recent advances in the theory of constant mean curvature surfaces within homogeneous 3-manifolds, including existence results and descriptions of $H$-laminations and CMC foliations in Riemannian manifolds.
Contribution
It provides a comprehensive overview of recent developments in the understanding of constant mean curvature surfaces and related structures in geometric analysis.
Findings
Summarizes key recent results in CMC surface theory
Discusses existence and classification of $H$-laminations
Explores CMC foliations in Riemannian manifolds
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 -laminations and CMC foliations of Riemannian -manifolds.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Point processes and geometric inequalities