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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, Volume 15, Issue 2, Pages 160–167
DOI: https://doi.org/10.18500/1816-9791-2015-15-2-160-167 (Mi isu577) 		 
Mathematics

Asymptotic ratio of harmonic measures of slit sides

D. V. Prokhorov, D. V. Ukrainskii

Saratov State University, 83, Astrakhanskaya st., 410012, Saratov, Russia
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DOI: https://doi.org/10.18500/1816-9791-2015-15-2-160-167
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.
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: English
Citation: D. V. Prokhorov, D. V. Ukrainskii, “Asymptotic ratio of harmonic measures of slit sides”, Izv. Saratov Univ. Math. Mech. Inform., 15:2 (2015), 160–167
Citation in format AMSBIB
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\by D.~V.~Prokhorov, D.~V.~Ukrainskii
\paper Asymptotic ratio of harmonic measures of slit sides
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2015
\vol 15
\issue 2
\pages 160--167
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\crossref{https://doi.org/10.18500/1816-9791-2015-15-2-160-167}
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    		Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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