Harmonic measures of slit sides perpendicular to the domain boundary

Details Harmonic measures of slit sides perpendicular to the domain boundary Harmonic measures of slit sides perpendicular to the domain boundary

2012-01-23

arxiv.org/abs/1201.4750v1

Mathematics

Complex Variables

8 pages

Scientific paper

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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