Geometric rigidity for sequences of W2,2 conformal immersions

Nguyen, Huy The (2014) Geometric rigidity for sequences of W2,2 conformal immersions. Calculus of Variations and Partial Differential Equations, 49 3-4: 1337-1357. doi:10.1007/s00526-013-0624-6


Author Nguyen, Huy The
Title Geometric rigidity for sequences of W2,2 conformal immersions
Formatted title
Geometric rigidity for sequences of W2,2 conformal immersions
Journal name Calculus of Variations and Partial Differential Equations   Check publisher's open access policy
ISSN 0944-2669
1432-0835
Publication date 2014-03-01
Year available 2013
Sub-type Article (original research)
DOI 10.1007/s00526-013-0624-6
Open Access Status Not Open Access
Volume 49
Issue 3-4
Start page 1337
End page 1357
Total pages 21
Place of publication Heidelberg, Germany
Publisher Springer
Language eng
Formatted abstract
We analyse sequences of discs conformally immersed in Rn with energy ∫D|Ak|2≤γn , where γn=8π if n=3 and γn=4π when n≥4 . We show that if such sequences do not weakly converge to a conformal immersion, then by a sequence of dilations we obtain a complete minimal surface with bounded total curvature, either Enneper’s minimal surface if n=3 or Chen’s minimal graph if n≥4 . In the papers, (Kuwert and Li, Comm Anal Geom 20(2), 313–340, 2012; Rivière, Adv Calculus Variations 6(1), 1–31, 2013) it was shown that if a sequence of immersed tori diverges in moduli space then lim infk→∞W(fk)≥8π . We apply the above analysis to show that in R3 if the sequence diverges so that limk→∞W(fk)=8π then there exists a sequence of Möbius transforms σk such that σkfk converges weakly to a catenoid.
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 2014 Collection
 
Versions
Version Filter Type
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
Google Scholar Search Google Scholar
Created: Tue, 11 Mar 2014, 10:34:33 EST by System User on behalf of School of Mathematics & Physics