Openness and Discreteness of Mappings of Finite Distortion on Carnot Groups

被引：3

作者：

Basalaev, S. G. ^{[1
]}

Vodopyanov, S. K. ^{[1
]}

机构：

[1] Sobolev Inst Math, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2023年 / 64卷 / 06期

关键词：

mappings of finite distortion; discreteness; openness; SPACES;

D O I：

10.1134/S0037446623060046

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a mapping of finite distortion f : Omega -> G in a domain Omega of an H-type Carnot group G is continuous, open, and discrete provided that the distortion function K(x) of f belongs to L-p,L-loc (Omega) for some p > nu - 1. In fact, the proof is suitable for each Carnot group provided it has a nu-harmonic function of the form log rho, where the homogeneous norm rho is C-2-smooth.

引用

页码：1289 / 1296

页数：8

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[2]

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[3]

Bonfiglioli A, 2007, SPRINGER MONOGR MATH, P3

[4]

Folland G. B., 1982, MATH NOTES, V28