Compactness of surfaces in \(\mathbb{R}^n\) with small total curvature
type: Item
instance of: scholarly article
title: Compactness of surfaces in \(\mathbb{R}^n\) with small total curvature
zbMATH Open document ID: 1492.53009
author: Yanyan Li
published in: The Journal of Geometric Analysis
publication date: 2021-08-31T00:00:00Z
review text: The authors study the compactness and local structure of immersed surfaces in the unit ball of \(\mathbb{R}^n\) with uniformly bounded area and small total curvature. A fundamental convergence theorem is obtained in intrinsic \(L_p\)-topology and extrinsic \(W^{2,2}\)-weak topology. To prove this theorem, the authors introduce a new quantity called ``isothermal radius'' and estimate its lower bound. In the end, the authors give two applications, one is bi-Lipschitz parametrization and Leon Simon's decomposition theorem, and the other one is Hélein's convergence theorem.
reviewed by: Hang Chen
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 57R42
zbMATH DE Number: 7388788
zbMATH Keywords: isothermal radius
zbMATH Keywords: compactness
zbMATH Keywords: bi-Lipschitz parametrization
zbMATH Keywords: total curvature
MaRDI profile type: Publication
full work available at URL: s12220-020-00583-z
OpenAlex ID: W3126246116
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DOI: 10.1007/S12220-020-00583-Z
description: scientific article; zbMATH DE number 7388788