Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

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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, EDN: TXMFQT

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Асимптотическое отношение гармонических мер сторон разреза

Prokhorov Dmitri Valentinovich, Saratov State University
Ukrainskii Dmitri Vladimirovich, Saratov State University

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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