EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.)
Vol. 75(89), pp. 147–171 (2004)

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DIRICHLET'S PRINCIPLE, DISTORTION AND RELATED PROBLEMS FOR HARMONIC MAPPINGS

Miodrag Mateljevic

Matematicki fakultet, Beograd, Serbia

Abstract: We give a short review of some known and new results related to harmonic maps. In particular, we generalize classical Dirichlet's principle, area theorem, theorems of uniqueness of harmonic maps, Bloch theorem, estimates for the modulus of the derivatives of harmonic univalent mappings, etc. We use different tools: Dirichlet's principle, minimizing sequences, different versions of Reich–Strebel inequality, area theorem, etc. Also, a comprehensive outline of proofs for most of new results is given.

Classification (MSC2000): 32G15; 30C45, 30C80, 30F60

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Electronic fulltext finalized on: 27 Oct 2004. This page was last modified: 22 Feb 2005.

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