Problemy Analiza — Issues of Analysis
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Probl. Anal. Issues Anal.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Problemy Analiza — Issues of Analysis, 2023, Volume 12(30), Issue 3, paper published in the English version journal
DOI: https://doi.org/10.15393/j3.art.2023.14110 (Mi pa387) 		 
Planar harmonic mappings with a given Jacobian

S. Yu. Grafab, I. A. Nikitinca

a Tver State University, 35 Sadovyy per., Tver, 170002, Russia
b Petrozavodsk State University, 33 Lenina pr., Petrozavodsk, 185910, Russia
c Lomonosov Moscow State University, 1 Leninskie Gory, Moscow, 119991, Russia
Full-text PDF (527 kB)
References:
PDF
HTML
DOI: https://doi.org/10.15393/j3.art.2023.14110
Abstract: The article is devoted to the study of the Jacobians of sense-preserving harmonic mappings in the unit disk of the complex plane. The main result is a criterion for an infinitely differentiable positive function to be a Jacobian of some sense-preserving harmonic mapping. The relationship between a Jacobian of a harmonic mapping and the Schwarzian derivative of its dilatation is revealed. The structure of the set of harmonic mappings with a given Jacobian is described. The results are illustrated by examples. In conclusion, we consider an application of the main results of the article to the construction of variational formulas in classes of harmonic mappings with a given Jacobian.
Keywords: planar harmonic mappings, Jacobian, dilatation, Schwarzian derivative.
Received: 09.06.2023
Revised: 02.09.2023
Accepted: 07.09.2023
Document Type: Article
UDC: 517.572
MSC: 31A05
Language: English
Citation: S. Yu. Graf, I. A. Nikitin
Citation in format AMSBIB
\Bibitem{GraNik23}
\by S.~Yu.~Graf, I.~A.~Nikitin
\mathnet{http://mi.mathnet.ru/pa387}
\crossref{https://doi.org/10.15393/j3.art.2023.14110}
Linking options:
  • https://www.mathnet.ru/eng/pa387
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Problemy Analiza — Issues of Analysis
    Statistics & downloads:
    Abstract page:60
    Full-text PDF :32
    References:16
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024