Одељење за математику, 24. октобар 2014.

Наредни састанак Семинара биће одржан у петак, 24. октобра 2014. у сали 301ф Математичког института САНУ са почетком у 14h.

Предавач: Весна Манојловић, ФОН, Универзитет у Београду и Математички Институт САНУ

Наслов предавања: HARMONIC QUASICONFORMAL MAPPINGS IN DOMAINS IN $R^n$

Садржај: This talk is based on certain aspects of $hqc$ mappings in domains in $R^n$. Emphasis is given on a generalization of Pavlovi`{c}`s characterization of boundary mapping admitting $hqc$ extension to the unit disc, to the multidimensional setting.

Harmonic quasiconformal (briefly, $hqc$) mappings in the plane were studied first by O. Martio in 1968., today they are investigated both in the planar and the multidimensional setting from several different points of view. Among topics considered are: boundary behavior, including Holder and Lipschitz continuity and more general moduli of continuity, behavior with respect to natural metrics, especially quasihyperbolic metric, distortion estimates, bi-Lipschitz properties with respect to different metrics, characterization of boundary maps. Different tools are used : conformal moduli of curve families, Poisson kernels, estimates from the theory of second order elliptic operators, notions of capacity, subharmonic functions, Hilbert`s transformation. Both theories of harmonic mappings and quasiconformal mappings are well developed, it is of interest to consider how these results can be strengthened in presence of both harmonicity and quasiconformality. Some of the results are unexpected and elegant, e.g. preservation of boundary modulus of continuity in the unit ball, bi-Lipschitz property with respect to quasihyperbolic metric.


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