Quantitative rigidity results for conformal immersions

Lamm, Tobias and Nguyen, Huy The (2014) Quantitative rigidity results for conformal immersions. American Journal of Mathematics, 136 5: 1409-1440. doi:10.1353/ajm.2014.0033

Author Lamm, Tobias
Nguyen, Huy The
Title Quantitative rigidity results for conformal immersions
Journal name American Journal of Mathematics   Check publisher's open access policy
ISSN 1080-6377
Publication date 2014-10
Year available 2014
Sub-type Article (original research)
DOI 10.1353/ajm.2014.0033
Open Access Status
Volume 136
Issue 5
Start page 1409
End page 1440
Total pages 32
Place of publication Baltimore, United States
Publisher Johns Hopkins University Press
Collection year 2015
Language eng
Formatted abstract
In this paper we prove several quantitative rigidity results for conformal immersions of surfaces in ${\Bbb R}^n$ with bounded total curvature. We show that (branched) conformal immersions which are close in energy to either a round sphere, a conformal Clifford torus, an inverted catenoid, an inverted Enneper's minimal surface or an inverted Chen's minimal graph must be close to these surfaces in the $W^{2,2}$-norm. Moreover, we apply these results to prove a corresponding rigidity result for complete, connected and non-compact surfaces.
Keyword Conformal immersions
Quantitative rigidity
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
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Citation counts: TR Web of Science Citation Count  Cited 1 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 1 times in Scopus Article | Citations
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