On Quasiregualr Mappings and Domains with a Complete Conformal Metric.
Koebe Arcs and Quasiregular Mappings.
Quadruples and spatial quasiconformal mappings.
On Teichmüller's modulus problem in R...
On the uniqueness of sequential limits of quasiconformal mappings.
On the Iversen-Tsuji theorem quasiregular mappings.
Cluster sets and boundary behavior of quasiregular mappings.
Lindelöf-type theorems for quasiconformal and quasiregular mappings
Möbius metric in sector domains
The Möbius metric is studied in the cases, where its domain is an open sector of the complex plane. We introduce upper and lower bounds for this metric in terms of the hyperbolic metric and the angle of the sector, and then use these results to find bounds for the distortion of the Möbius metric under quasiregular mappings defined in sector domains. Furthermore, we numerically study the Möbius metric and its connection to the hyperbolic metric in polygon domains.
On Kaluza's sign criterion for reciprocal power series
T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzyż is applied.
On Kaluza’s sign criterion for reciprocal power series
T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzyż is applied.
Linear distortion of Hausdorff dimension and Cantor's function.
Let be a mapping from a metric space X to a metric space Y, and let α be a positive real number. Write dim (E) and H(E) for the Hausdorff dimension and the s-dimensional Hausdorff measure of a set E. We give sufficient conditions that the equality dim (f(E)) = αdim (E) holds for each E ⊆ X. The problem is studied also for the Cantor ternary function G. It is shown that there is a subset M of the Cantor ternary set such that H(M) = 1, with s = log2/log3 and dim(G(E)) = (log3/log2) dim (E), for every...
Removable singularities of -differential forms and quasiregular mappings.
The computation of capacity of planar condensers.
Stagnation zones for -harmonic functions on canonical domains.
On conformal dilatation in space.
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