Geodesic
Dirichlet's Principle, Distortion and Related Problems for Harmonic Mappings
Publications de l'Institut Mathématique, _N_S_75 (2004) no. 89, p. 147 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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.
DOI : 10.2298/PIM0475147M
Classification : 32G15 30C45 30C80 30F60
Keywords: Dirichlet's principle, harmonic mappings 
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     author = {Miodrag Mateljevi\'c},
     title = {Dirichlet's {Principle,} {Distortion} and {Related} {Problems} for {Harmonic} {Mappings}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {147 },
     year = {2004},
     volume = {_N_S_75},
     number = {89},
     doi = {10.2298/PIM0475147M},
     zbl = {1081.30022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0475147M/}
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Miodrag Mateljević. Dirichlet's Principle, Distortion and Related Problems for Harmonic Mappings. Publications de l'Institut Mathématique, _N_S_75 (2004) no. 89, p. 147 . doi: 10.2298/PIM0475147M

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