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Asymptotic ratio of harmonic measures of slit sides. (English. Russian summary) Zbl 1408.30031

Summary: 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.

MSC:

30C85 Capacity and harmonic measure in the complex plane
30C20 Conformal mappings of special domains
30C75 Extremal problems for conformal and quasiconformal mappings, other methods
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
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