On variational principles of conformal mappings

Dubinin, V.; Prilepkina, E.

doi:10.1090/S1061-0022-07-00955-7

On variational principles of conformal mappings
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by 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.

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