{"id":1791,"date":"2022-01-24T13:24:38","date_gmt":"2022-01-24T13:24:38","guid":{"rendered":"https:\/\/akademperiodyka.org.ua\/en\/?p=1791"},"modified":"2025-07-10T08:51:24","modified_gmt":"2025-07-10T08:51:24","slug":"infinitesimal_geometry_of_spatial_mappings","status":"publish","type":"post","link":"https:\/\/akademperiodyka.org.ua\/en\/books\/infinitesimal_geometry_of_spatial_mappings\/","title":{"rendered":"Infinitesimal Geometry of Spatial Mappings"},"content":{"rendered":"
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Project: Ukrainian scientific book in a foreign language<\/div>\n<\/div>\n
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Authors: V.Ya. Gutlyanskii, V.I. Ryazanov<\/strong><\/div>\n<\/div>\n
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Year: 2013<\/div>\n<\/div>\n
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Pages: 188<\/div>\n<\/div>\n
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ISBN: 978-966-360-243-1<\/div>\n<\/div>\n
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Publication Language: English<\/div>\n<\/div>\n
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Publisher: PH “Akademperiodyka”<\/div>\n<\/div>\n
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Place Published: Kyiv<\/div>\n<\/div>\n
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doi: https:\/\/doi.org\/10.15407\/akademperiodyka.243.188<\/a><\/div>\n<\/div>\n<\/div>\n<\/article>\n<\/div>\n<\/div>\n<\/section>\n
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This book is devoted to the recent advances in the theory of local topological and geometric properties of mappings in n-dimensional Euclidean space. Quasiconformal, and quasiregular bi-Lipschitz mappings and the methods to study local behavior of this mappings without differentiability assumptions form the core of the book. In Part 1 the reader will find the necessary terminology, elementary facts and basic properties for such mappings. In Part 2 the fundamental concept of infinitesimal space quasiregular mapping at a point is introduced and its structure is described. The developed theory is applied in Part 3 to the study of local and boundary behavior of spatial mappings, their regularity, H\u00f6lder\u2019s and Lipschitz\u2019s continuity. It\u2019s shown that the local injectivity of a mapping display in space is intimately connected to the BMO property of its dilatation tensor.<\/div>\n
This book is addressed to experts in modern geometric function theory as well as to, educators and the beginning researchers graduate students with a year\u2019s background in real and complex variables seeking access to research topics.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<\/div>\n<\/div>\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Project: Ukrainian scientific book in a foreign language Authors: V.Ya. Gutlyanskii, V.I. Ryazanov Year: 2013 Pages: 188 ISBN: 978-966-360-243-1 Publication Language: English Publisher: PH “Akademperiodyka” Place Published: Kyiv doi: https:\/\/doi.org\/10.15407\/akademperiodyka.243.188 This book is devoted to the recent advances in the theory of local topological and geometric properties of mappings in n-dimensional Euclidean space. Quasiconformal, and […]<\/p>\n","protected":false},"author":1,"featured_media":1792,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,21,24],"tags":[],"class_list":["post-1791","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-books","category-scientific_monographs","category-ukrainian_scientifical_book"],"_links":{"self":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts\/1791","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/comments?post=1791"}],"version-history":[{"count":4,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts\/1791\/revisions"}],"predecessor-version":[{"id":3552,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts\/1791\/revisions\/3552"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/media\/1792"}],"wp:attachment":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/media?parent=1791"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/categories?post=1791"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/tags?post=1791"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}