Limit leaves of a CMC lamination are stable

2008/01/28 by William H. Meeks, William H. Meeks III, Meeks, William H. +4 · 2 citations
Arts and Humanities · Mathematics · #49Q05 #53A10 #53C42 #Cultural Heritage Materials Analysis #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:49Q05 #msc:53A10 #msc:53C42

paper · pdf · doi:10.48550/arxiv.0801.4345

10 pages, 3 figures, replacement: minor changes in the introduction + notation

openalex publication_date 2008/01/28 · arxiv created 2008/02/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose \cal L is a lamination of a Riemannian manifold by hypersurfaces with the same constant mean curvature. We prove that every limit leaf of \cal L is stable for the Jacobi operator. A simple but important consequence of this result is that the set of stable leaves of \cal L has the structure of a lamination.

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• Properly embedded minimal planar domains with infinite topology are Riemann minimal examples
• Contractible 3-manifold and Positive scalar curvature (I)
• On the moduli of constant mean curvature cylinders of finite type in the 3-sphere

Related

• Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces
• Limit lamination theorems for H-surfaces
• The canonical lamination calibrated by a cohomology class
• Persistence of laminations
• Limit lamination theorem for H-disks