On variational principles of conformal mappings

V. N. Dubinin ; E. G. Prilepkina

Algebra i analiz, Tome 18 (2006) no. 3, pp. 39-62.

Résumé

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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