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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

On variational principles of conformal mappings


Authors: V. N. Dubinin and E. G. Prilepkina
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 18 (2006), nomer 3.
Journal: St. Petersburg Math. J. 18 (2007), 373-389
MSC (2000): Primary 30C70, 30C85
DOI: https://doi.org/10.1090/S1061-0022-07-00955-7
Published electronically: April 10, 2007
MathSciNet review: 2255850
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Abstract: Refinements and generalizations of the classical variational principles of conformal mappings are presented; mainly, they follow from potential theory and symmetrization. Part of the results can be viewed as properties of Robin functions and Robin capacities, and also as distortion theorems for univalent functions in finitely connected domains.


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Additional Information

V. N. Dubinin
Affiliation: Institute of Applied Mathematics, Far-East Branch, Russian Academy of Sciences, Ul. Radio 7, Vladivostok, 690041, Russia
Email: dubinin@iam.dvo.ru

E. G. Prilepkina
Affiliation: Institute of Applied Mathematics, Far-East Branch, Russian Academy of Sciences, Ul. Radio 7, Vladivostok, 690041, Russia
Email: pril@mail.primorye.ru

DOI: https://doi.org/10.1090/S1061-0022-07-00955-7
Keywords: Variational principles, conformal mapping, distortion theorems, univalent functions, Robin function, Robin capacity, the capacity of a condenser, majorant domains, symmetrization, polarization.
Received by editor(s): February 22, 2006
Published electronically: April 10, 2007
Additional Notes: This research was supported by the “Leading research school” program (grant no. Sh-9004.2006.1), by RFBR (grant no. 05-01-00099), and by FEB RAS (grant no. 06-III-A-01-013).
Dedicated: Dedicated to the 100th anniversary of Gennadiĭ Mikhailovich Goluzin’s birth
Article copyright: © Copyright 2007 American Mathematical Society

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