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

[41] ON THE ORBITAL STABILITY OF A FAMILY OF TRAVELLING WAVES FOR THE CUBIC SCHRODINGER EQUATION ON THE HEISENBERG GROUP
Gassot, Louise
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 2021, 149 (01): : 15 - 54
[42] Quasiconvexity in the Heisenberg group
Herron, David A.
Lukyanenko, Anton
Tyson, Jeremy T.
GEOMETRIAE DEDICATA, 2018, 192 (01) : 157 - 170
[43] Optimization in the Heisenberg group
Calogero, A.
Carcano, G.
Pini, R.
OPTIMIZATION, 2006, 55 (04) : 387 - 403
[44] HYPOELLIPTICITY ON THE HEISENBERG GROUP
MILLER, KG
JOURNAL OF FUNCTIONAL ANALYSIS, 1979, 31 (03) : 306 - 320
[45] Quasiconvexity in the Heisenberg group
David A. Herron
Anton Lukyanenko
Jeremy T. Tyson
Geometriae Dedicata, 2018, 192 : 157 - 170
[46] Geodesics in the Heisenberg Group
Hajlasz, Piotr
Zimmerman, Scott
ANALYSIS AND GEOMETRY IN METRIC SPACES, 2015, 3 (01): : 325 - 337
[47] Multipliers on the Heisenberg group
Veneruso, A
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2000, 3A : 229 - 232
[48] Solvability on the Heisenberg group
Karadzhov, GE
MATHEMATISCHE NACHRICHTEN, 2006, 279 (04) : 400 - 414
[49] ON THE QUADRATIC HEISENBERG GROUP
Accardi, Luigi
Ouerdiane, Habib
Rebei, Habib
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2010, 13 (04) : 551 - 587
[50] THE EMBEDDINGS OF THE HEISENBERG GROUP INTO THE CREMONA GROUP
Deserti, Julie
GLASGOW MATHEMATICAL JOURNAL, 2022, 64 (01) : 243 - 251

← 1 2 3 4 5 →