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QUANTITATIVE RIGIDITY RESULTS FOR CONFORMAL IMMERSIONS.

Authors :
LAMM, TOBIAS
HUY THE NGUYEN
Source :
American Journal of Mathematics. Oct2014, Vol. 136 Issue 5, p1409-1440. 33p.
Publication Year :
2014

Abstract

In this paper we prove several quantitative rigidity results for conformal immersions of surfaces in ℝn 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 W2,2-norm. Moreover, we apply these results to prove a corresponding rigidity result for complete, connected and non-compact surfaces. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00029327
Volume :
136
Issue :
5
Database :
Academic Search Index
Journal :
American Journal of Mathematics
Publication Type :
Academic Journal
Accession number :
99203778
Full Text :
https://doi.org/10.1353/ajm.2014.0033