Topological Properties of Mappings with Finite Distortion on Carnot Groups

被引：0

作者：

Isangulova, D. V. ^{[1
]}

机构：

[1] Novosibirsk State Univ, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2024年 / 65卷 / 01期

关键词：

Carnot group; mapping with finite distortion; quasilightness; openness; discreteness; 517.54; BOUNDED DISTORTION; DIFFERENTIABILITY; SPACES;

D O I：

10.1134/S0037446624010063

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that every mapping with finite distortion on a Carnot group is open and discrete provided that it is quasilight and the distortion coefficient is integrable. Also, we estimate the Hausdorff dimension of the preimages of points for mappings on a Carnot group with a bounded multiplicity function and summable distortion coefficient. Furthermore, we give some example showing that the obtained estimates cannot be improved.

引用

页码：48 / 61

页数：14

共 26 条

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[Anonymous], 2000, P AN GEOM SOB I MATH

[2] POINTWISE DIFFERENTIABILITY AND ABSOLUTE CONTINUITY [J].