On variational principles of conformal mappings
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V. N. Dubinin and E. G. Prilepkina
Translated by: S. V. Kislyakov - St. Petersburg Math. J. 18 (2007), 373-389
- DOI: https://doi.org/10.1090/S1061-0022-07-00955-7
- Published electronically: April 10, 2007
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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.References
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Bibliographic 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
- 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).
- © Copyright 2007 American Mathematical Society
- 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
- MathSciNet review: 2255850
Dedicated: Dedicated to the 100th anniversary of Gennadiĭ Mikhailovich Goluzin’s birth