Quasi-variance of the modulus of homotopical classes of curves and Teichmuller’s problem
Results are obtained on the quasiconformal distortion of the modulus of one and several classes of punctiform curves on the plane. The relationship to Teichmuller's problem for a quadruple of points and the homotopic properties of extremal mappings are studied. In particular, the variation...
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| Date: | 1991 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1991
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9611 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865795317272674304 |
|---|---|
| author | Vasiliev , A. Yu. Васильев , А. Ю. |
| author_facet | Vasiliev , A. Yu. Васильев , А. Ю. |
| author_institution_txt_mv | [
{
"author": "А. Ю. Васильев ",
"institution": "Саратов. ин-т механизации сел. хоз-ва"
}
] |
| author_sort | Vasiliev , A. Yu. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-10-09T12:05:28Z |
| description | Results are obtained on the quasiconformal distortion of the modulus of one and several classes of punctiform curves on the plane. The relationship to Teichmuller's problem for a quadruple of points and the homotopic properties of extremal mappings are studied. In particular, the variation of the minimum deviations produced in different motions of one labeled point is studied. |
| first_indexed | 2026-03-24T03:46:11Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9611 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:46:11Z |
| publishDate | 1991 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-96112025-10-09T12:05:28Z Quasi-variance of the modulus of homotopical classes of curves and Teichmuller’s problem Квазиинвариантность модуля гомотопических классов кривых и задача Тейхмюллера Vasiliev , A. Yu. Васильев , А. Ю. - Results are obtained on the quasiconformal distortion of the modulus of one and several classes of punctiform curves on the plane. The relationship to Teichmuller's problem for a quadruple of points and the homotopic properties of extremal mappings are studied. In particular, the variation of the minimum deviations produced in different motions of one labeled point is studied. Получены результаты о квазиконформном искажении модуля одного и нескольких гомотопических классов кривых на плоскости с проколами. Исследуются связи с задачей Тейхмюллера о четверке точек, гомотопические свойства экстремальных отображений; В частности, изучается изменение минимума отклонения при различных движениях одной отмененной точки. Одержані результати про квазіконформне спотворення модуля одного і декількох гомо-топічних класів кривих на поверхні з дірками. Досліджуються зв’язки з задачею Тейхмюллера про четвірку точок, гомотопічні властивості екстремальних відображень. Зокрема, вивчається зміна мінімума відхилення при різних рухах однієї відміченої точки, Institute of Mathematics, NAS of Ukraine 1991-02-28 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/9611 Ukrains’kyi Matematychnyi Zhurnal; Vol. 43 No. 3 (1991); 329-336 Український математичний журнал; Том 43 № 3 (1991); 329-336 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/9611/10579 Copyright (c) 1991 А. Ю. Васильев |
| spellingShingle | Vasiliev , A. Yu. Васильев , А. Ю. Quasi-variance of the modulus of homotopical classes of curves and Teichmuller’s problem |
| title | Quasi-variance of the modulus of homotopical classes of curves and Teichmuller’s problem |
| title_alt | Квазиинвариантность модуля гомотопических классов кривых и задача Тейхмюллера |
| title_full | Quasi-variance of the modulus of homotopical classes of curves and Teichmuller’s problem |
| title_fullStr | Quasi-variance of the modulus of homotopical classes of curves and Teichmuller’s problem |
| title_full_unstemmed | Quasi-variance of the modulus of homotopical classes of curves and Teichmuller’s problem |
| title_short | Quasi-variance of the modulus of homotopical classes of curves and Teichmuller’s problem |
| title_sort | quasi-variance of the modulus of homotopical classes of curves and teichmuller’s problem |
| topic_facet | - |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9611 |
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