Limit Lamination Theorems for H-surfaces

TY - JOUR

T1 - Limit Lamination Theorems for H-surfaces

AU - H. Meeks III, William

AU - Tinaglia, Giuseppe

PY - 2019/3/1

Y1 - 2019/3/1

N2 - In this paper we prove some general results for constant mean curvature lamination limits of certain sequences of compact surfaces M n embedded in ℝ 3 with constant mean curvature H 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.

AB - In this paper we prove some general results for constant mean curvature lamination limits of certain sequences of compact surfaces M n embedded in ℝ 3 with constant mean curvature H 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.

UR - http://www.scopus.com/inward/record.url?scp=85050164615&partnerID=8YFLogxK

U2 - 10.1515/crelle-2016-0038

DO - 10.1515/crelle-2016-0038

M3 - Article

SN - 0075-4102

VL - 2019

SP - 269

EP - 296

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

IS - 748

ER -