doiSerbia

Dirichlets principle, distortion and related problems for harmonic mappings

Mateljević Miodrag S. (Matematički fakultet, Beograd)

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, comprehensive outlines of proofs for most of new results are given.