15 citations · 27 across the 14 of their papers we have counts for
14 papers
Solutions of the Loewner equation with combined driving functions
Dmitri Prokhorov, Andrey Zakharov, Andrey Zherdev
The paper is devoted to the multiple chordal Loewner differential equation with different driving functions on two time intervals. We obtain exact implicit or explicit solutions to…
Value regions of univalent self-maps with two boundary fixed points
Pavel Gumenyuk, Dmitri Prokhorov
In this paper we find the exact value region of the point evaluation functional over the class of all holomorphic injective self-maps $f:\math…
Comformal mapping asymptotics at a cusp
Dmitri Prokhorov
We describe the asymptotic behavior of the mapping function at an analytic cusp compared with Kaiser's results for cusps with small perturbation of angles and the known explicit fo…
Approximation of sgn(x) on two symmetric intervals by rational functions with fixed poles
A. Lukashov, D. Prokhorov
Recently A. Eremenko and P. Yuditskii found explicit solutions of the best polynomial approximation problems of sgn(x) over two intervals in terms of conformal mappings onto specia…
Asymptotic ratio of harmonic measures of slit sides
Dmitri Prokhorov, Dmitrii Ukrainskii
The article is devoted to the geometry of solutions to the chordal Loewner equation which is based on the comparison of singular solutions and harmonic measures for the sides of a…
Loewner evolution and finite dimensional reductions of integrable systems
Maxim V. Pavlov, Dmitri Prokhorov, Alexander Vasil'ev +1
The Loewner equation is known as a one-dimensional reduction of the Benney chain as well as the dispersionless KP hierarchy. We propose a reverse process showing that time splittin…