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QUANTITATIVE RIGIDITY RESULTS FOR CONFORMAL IMMERSIONS.
- 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