Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

singular solution

Асимптотическое отношение гармонических мер сторон разреза

The article is devoted to the geometry of solutions to the chordal Löwner equation which is based on the comparison of singular solutions and harmonic measures for the sides of a slit in the upper half-plane generated by a driving term. An asymptotic ratio for harmonic measures of slit sides is found for a slit which is tangential to a straight line under a given angle, and for a slit with high order tangency to a circular arc tangential to the real axis.

Integrability of a Partial Case of the Lowner Equation

We give a quadrature solution to the partial case of the Lowner¨ equation for the upper half-plane.