Mappings with Direct and Inverse Poletsky Inequalities

Evgeny Sevost'yanov

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Hardback

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English

Springer International Publishing AG
18 November 2023

Calculus & mathematical analysis; Complex analysis, complex variables

Series: Developments in Mathematics

The monograph is devoted to the use of the moduli method in mapping theory, in particular, the meaning of direct and inverse modulus inequalities and their possible applications. The main goal is the development of a modulus technique in the Euclidean space and some metric spaces (manifolds, surfaces, quotient spaces, etc.). Particular attention is paid to the local and boundary behavior of mappings, as well as to obtaining modulus inequalities for some classes. The reader is invited to familiarize himself with all the main achievements of the author, synthesized in this book. The results presented here are of a high scientific level, are new and have no analogues in the world with such a degree of generality.

By: Evgeny Sevost'yanov
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2023 ed.
Volume: 78
Dimensions: Height: 235mm, Width: 155mm,
Weight: 834g
ISBN: 9783031454172
ISBN 10: 3031454170
Series: Developments in Mathematics
Pages: 433
Publication Date: 18 November 2023
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Evgeny Sevost’yanov is Head of Department of Mathematical Analysis, Business Analysis and Statistics at Zhytomyr Ivan Franko State University, Ukraine. His research interests include mapping theory and its applications to equations with partitional derivatives. The main results of E. Sevost’yanov concern the local and boundary behavior of mappings, mappings of metric spaces and Riemannian manifolds, quotient spaces and Riemannian surfaces. From 2002 up to now E. Sevost’yanov works as a researcher in Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine (located in Donetsk up to 2014, and in Slov’yans’k from 2014). From 2014 up to now E. Sevost’yanov works in Zhytomyr Ivan Franko State University, which belongs to the system of Ministry of Education and Science of Ukraine. Candidate of Physical and Mathematical Sciences (2006), Doctor of Physical and Mathematical Sciences (2013), Senior Researcher (2011).

Reviews for Mappings with Direct and Inverse Poletsky Inequalities

“The book may be of interest for teachers and researchers in complex analysis and, more generally, those in function theory. Since 2009, there have been a great volume of facts derived from this theory of mappings, particularly those defined by modular inequalities. Therefore, such a book as this is very useful. The style of the author is that of a professor teaching a course to students, very clear; he tries to be as self-contained … .” (Mihai Cristea, Mathematical Reviews, February, 2025)