QUANTITATIVE RIGIDITY RESULTS FOR CONFORMAL IMMERSIONS

被引：5
作者：
Lamm, Tobias [1 ]
Huy The Nguyen [2 ]
机构：
[1] Karlsruhe Inst Technol, Inst Anal, D-76133 Karlsruhe, Germany
[2] Univ Queensland, Sch Math & Phys, Brisbane, Qld 4072, Australia
来源：
AMERICAN JOURNAL OF MATHEMATICS | 2014年 / 136卷 / 05期
关键词：
GEOMETRIC RIGIDITY; COMPLETE-SURFACES; MINIMAL SURFACES; WILLMORE; 3-MANIFOLDS; MINIMIZERS; EXISTENCE; THEOREM;
D O I：
10.1353/ajm.2014.0033
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we prove several quantitative rigidity results for conformal immersions of surfaces in 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,W-2-norm. Moreover, we apply these results to prove a corresponding rigidity result for complete, connected and non-compact surfaces.
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收藏
页码：1409 / 1440
页数：32
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