Stability of isometric maps in the Heisenberg group

被引：0

作者：

Arcozzi, Nicola ^{[1
]}

Morbidelli, Daniele ^{[1
]}

机构：

[1] Univ Bologna, Dipartmento Matemat, I-40127 Bologna, Italy

来源：

COMMENTARII MATHEMATICI HELVETICI | 2008年 / 83卷 / 01期

关键词：

Heisenberg group; subRiemannian geometry; biLipschitz maps;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove approximation results for biLipschitz maps in the Heisenberg group. Namely, we show that a biLipschitz map with biLipschitz constant close to one can be pointwise approximated, quantitatively in any fixed ball, by an isometry. This leads to an approximation in BMO norm for the map's Pansu derivative. We also prove that a global quasigeodesic can be approximated by a geodesic on any fixed segment.

引用

页码：101 / 141

页数：41

共 50 条

[1] Isometric immersions into a homogeneous Lorentzian Heisenberg group and rigidity
Barbero Lodovici, Sinue Dayan
Manfio, Fernando
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2009, 147 : 185 - 204
[2] Uniformly Quasiregular Maps on the Compactified Heisenberg Group
Zoltán M. Balogh
Katrin Fässler
Kirsi Peltonen
Journal of Geometric Analysis, 2012, 22 : 633 - 665
[3] Uniformly Quasiregular Maps on the Compactified Heisenberg Group
Balogh, Zoltan M.
Faessler, Katrin
Peltonen, Kirsi
JOURNAL OF GEOMETRIC ANALYSIS, 2012, 22 (03) : 633 - 665
[4] Quasiregular maps and the conductivity equation in the Heisenberg group
Isopoussu, Anton
Peltonen, Kirsi
Tyson, Jeremy T.
IN THE TRADITION OF AHLFORS-BERS, VI, 2013, 590 : 61 - 75
[5] Hardy spaces and quasiconformal maps in the Heisenberg group
Adamowicz, Tomasz
Faessler, Katrin
JOURNAL OF FUNCTIONAL ANALYSIS, 2023, 284 (06)
[6] Lifts of Lipschitz maps and horizontal fractals in the Heisenberg group
Balogh, Zoltan M.
Hoefer-Isenegger, Regula
Tyson, Jeremy T.
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2006, 26 : 621 - 651
[7] Problem about the compactness of the maps for the Heisenberg group target
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Shanghai Ligong Daxue Xuebao, 2006, 4 (317-319):
[8] Stability of Mappings with Bounded Distortion on the Heisenberg Group
N. S. Dairbekov
Siberian Mathematical Journal, 2002, 43 : 223 - 234
[9] A quantitative stability theorem for convolution on the Heisenberg group
O'Neill, Kevin
REVISTA MATEMATICA IBEROAMERICANA, 2021, 37 (05) : 1861 - 1884
[10] Stability of mappings with bounded distortion on the Heisenberg group
Dairbekov, NS
SIBERIAN MATHEMATICAL JOURNAL, 2002, 43 (02) : 223 - 234

← 1 2 3 4 5 →