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arXiv · 1408.0882

Asymptotic ratio of harmonic measures of slit sides

Dmitri Prokhorov·Dmitrii Ukrainskii
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Abstract

The article is devoted to the geometry of solutions to the chordal Loewner 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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Dmitri Prokhorov, Dmitrii Ukrainskii. 2014-08-05. Asymptotic ratio of harmonic measures of slit sides. https://arxiv.org/abs/1408.0882

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