Frequency of Sobolev dimension distortion of horizontal subgroups in Heisenberg groups

被引：0

作者：

Balogh, Zoltan M. ^{[1
]}

Tyson, Jeremy T. ^{[2
]}

Wildrick, Kevin ^{[1
]}

机构：

[1] Univ Bern, Math Inst, Sidlerstr 5, CH-3012 Bern, Switzerland

[2] Univ Illinois, Dept Math, 1409 W Green St, Urbana, IL 61801 USA

来源：

ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE | 2017年 / 17卷 / 02期

基金：

瑞士国家科学基金会;

关键词：

QUASI-CONFORMAL MAPPINGS; METRIC MEASURE-SPACES; CARNOT GROUPS; SUBSPACES; GEOMETRY; IMAGES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the behavior of Sobolev mappings defined on the sub-Riemannian Heisenberg groups with respect to foliations by left cosets of a horizontal homogeneous subgroup. Our main result provides a quantitative estimate, in terms of Hausdorff dimension, of the size of the set of cosets whose dimension is raised under such mappings. Our approach unifies ideas of Gehring and Mostow about the absolute continuity of quasiconformal mappings with Mattila's projection and slicing machinery.

引用

页码：655 / 683

页数：29

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