Tchebotaröv’s extremal problem
We give the complete solution of the extremal problem posed by N.G. Tchebotaröv in 20th of the last century, and we establish explicit parametric formulae for the extremals.
Teichmüller spaces are not starlike.
The Brothers Riesz theorem in and Laplace series.
The Douady-Earle extension of quasihomographies
Quasihomography is a useful notion to represent a sense-preserving automorphism of the unit circle T which admits a quasiconformal extension to the unit disc. For K ≥ 1 let denote the family of all K-quasihomographies of T. With any we associate the Douady-Earle extension and give an explicit and asymptotically sharp estimate of the norm of the complex dilatation of .
The hyperbolic Gauss map and quasiconformal reflections.
The integral means spectrum for lacunary series.
The law of the iterated logarithm for locally univalent functions.
Topological invariance of the Collet–Eckmann property for S-unimodal maps
We prove that if f, g are smooth unimodal maps of the interval with negative Schwarzian derivative, conjugated by a homeomorphism of the interval, and f is Collet-Eckmann, then so is g.
Two applications of one Robertson's results
Two criteria for univalency.
Typically real functions and typically real derivatives.
Typically real logharmonic mappings.