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.
Techniques of the differential subordination for domains bounded by conic sections.
The Asymptotic Value of the Circle-Packing Rigidity Constants sn .
The Bergman and Schiffer transforms on weighted norm spaces
The Cauchy Kernel, the Szegö Kernel, and the Riemann Mapping Function.
The Löwner-Kufarev representations for domains with analytic boundaries
We consider the Löwner-Kufarev differential equations generating univalent maps of the unit disk onto domains bounded by analytic Jordan curves. A solution to the problem of the maximal lifetime shows how long a representation of such functions admits using infinitesimal generators analytically extendable outside the unit disk. We construct a Löwner-Kufarev chain consisting of univalent quadratic polynomials and compare the Löwner-Kufarev representations of bounded and arbitrary univalent functions....
The Schwarzian derivative for conformal maps.
Topics form classical theory of conformal mapping