Cite this article as:

Prokhorov D. V., Ukrainskii D. V. Асимптотическое отношение гармонических мер сторон разреза . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2015, vol. 15, iss. 2, pp. 160-166. DOI: https://doi.org/10.18500/1816-9791-2015-15-2-160-167

Language: 
Russian
Heading: 
Mathematics
UDC: 
517.54

Асимптотическое отношение гармонических мер сторон разреза

Authors: 
Prokhorov Dmitri Valentinovich, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , ProkhorovDV@info.sgu.ru
Ukrainskii Dmitri Vladimirovich, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , D.V.Ukrainskiy@gmail.com
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.

Key words: 
Löwner equation, singular solution, harmonic measure, half-plane capacity
DOI: 
https://doi.org/10.18500/1816-9791-2015-15-2-160-167
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