Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Prokhorov D. V., Ukrainskii D. V. Асимптотическое отношение гармонических мер сторон разреза. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, vol. 15, iss. 2, pp. 160-166. DOI: 10.18500/1816-9791-2015-15-2-160-167

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
11.06.2015
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Russian
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UDC: 
517.54

Асимптотическое отношение гармонических мер сторон разреза

Autors: 
Prokhorov Dmitri Valentinovich, Saratov State University
Ukrainskii Dmitri Vladimirovich, Saratov State University
Abstract: 

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.

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