Geodesic
Asymptotic ratio of harmonic measures of slit sides
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 160-167

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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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     author = {D. V. Prokhorov and D. V. Ukrainskii},
     title = {Asymptotic ratio of harmonic measures of slit sides},
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D. V. Prokhorov; D. V. Ukrainskii. Asymptotic ratio of harmonic measures of slit sides. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 160-167. http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a4/