Author:
Meeks III William H.,Tinaglia Giuseppe
Abstract
AbstractIn this paper we prove some general results for constant mean curvature lamination limits of certain sequences of compact surfacesM_{n}embedded in\mathbb{R}^{3}with constant mean curvatureH_{n}and fixed finite genus, when the boundaries of these surfaces tend to infinity. Two of these theorems generalize to the non-zero constant mean curvature case, similar structure theorems by Colding and Minicozzi in [6, 8] for limits of sequences of minimal surfaces of fixed finite genus.
Funder
National Science Foundation
Engineering and Physical Sciences Research Council
Subject
Applied Mathematics,General Mathematics
Reference74 articles.
1. One-sided curvature estimates for H-disks;Preprint,2014
2. The Calabi-Yau conjectures for embedded surfaces;Ann. of Math.,2008
3. The space of embedded minimal surfaces of fixed genus in a 3-manifold. I. Estimates off the axis for disks;Ann. of Math.,2004
4. Topologie et courbure des surfaces minimales de ℝ3\mathbb{R}^{3};Ann. of Math. (2),1997