TY - JOUR

T1 - Topological Properties of Mappings with Finite Distortion on Carnot Groups

AU - Исангулова, Дарья Васильевна

N1 - The work is supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2022–282 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2024/1

Y1 - 2024/1

N2 - We prove thatevery mapping with finite distortion on a Carnot groupis open and discrete provided that it is quasilight and the distortion coefficient is integrable.Also, we estimate the Hausdorff dimension of the preimages of pointsfor mappings on a Carnot groupwith a bounded multiplicity functionand summable distortion coefficient.Furthermore, we give some example showing thatthe obtained estimates cannot be improved.

AB - We prove thatevery mapping with finite distortion on a Carnot groupis open and discrete provided that it is quasilight and the distortion coefficient is integrable.Also, we estimate the Hausdorff dimension of the preimages of pointsfor mappings on a Carnot groupwith a bounded multiplicity functionand summable distortion coefficient.Furthermore, we give some example showing thatthe obtained estimates cannot be improved.

KW - 517.54

KW - Carnot group

KW - discreteness

KW - mapping with finite distortion

KW - openness

KW - quasilightness

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85184421008&origin=inward&txGid=7c0255dc2c5372a4d35a90a5d3299c7f

UR - https://www.mendeley.com/catalogue/961cf449-5bb2-316a-bc1f-f253b9669aa3/

U2 - 10.1134/S0037446624010063

DO - 10.1134/S0037446624010063

M3 - Article

VL - 65

SP - 48

EP - 61

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 1

ER -