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arxiv: 1201.4750 · v1 · pith:MGAJB4N7new · submitted 2012-01-23 · 🧮 math.CV

Harmonic measures of slit sides perpendicular to the domain boundary

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keywords harmonicmeasuressidesslitperpendicularsolutionsarticleasymptotically
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The article is devoted to the geometry of solutions to the chordal Loewner equation which is based on comparison of singular solutions and harmonic measures for the sides of a slit in domains generated by a driving term. It is proved that harmonic measures of two sides of a slit in the upper half-plane which is perpendicular to the real axis are asymptotically equal to each other.

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