The space of embedded minimal surfaces of fixed genus in a 3-manifold. III: Planar domains
type: Item
instance of: scholarly article
title: The space of embedded minimal surfaces of fixed genus in a 3-manifold. III: Planar domains
zbMATH Open document ID: 1076.53068
published in: Annals of Mathematics. Second Series
publication date: 2005-04-18T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0210141
full work available at URL: https://projecteuclid.org/euclid.annm/1111770728
review text: The paper under review is the third one in a series where the authors describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed \(3\)-manifold [see Part I, Ann. Math. (2) 160, No. 1, 27--68 (2004; Zbl 1070.53031); II, ibid. 160, No. 1, 69--92 (2004; Zbl 1070.53032); IV, ibid. 160, No. 2, 573--615 (2004; Zbl 1076.53069)]. There are two main themes in this paper. The first is that stability leads to improved curvature estimates. This allows them to find large graphical regions. These graphical regions lead to two possiblities: (1) they ``close up'' to form a graph, (2) a multi-valued graph froms. The second theme is that in certain important cases they can rule out the formation of multi-valued graph.
reviewed by: Haizhong Li
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 58D10
Mathematics Subject Classification ID: 58E12
zbMATH DE Number: 2157796
zbMATH Keywords: embedded minimal surface
zbMATH Keywords: genus
zbMATH Keywords: planar domain
author: Tobias Holck Colding
author: William P. II Minicozzi
MaRDI profile type: Publication
OpenAlex ID: W1989100446
arXiv ID: math/0210141
DOI: 10.4007/ANNALS.2004.160.523
description: scientific article