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Exponential driving function for the Löwner equation

We consider the chordal Löwner differential equation with the model driving function $\root3\of t$. Holomorphic and singular solutions are represented by their series. It is shown that a disposition of values of different singular and branching solutions is monotonic, and solutions to the Löwner equation map slit domains onto the upper half-plane. The slit is a $C^1$-curve. We give an asymptotic estimate for the ratio of harmonic measures of the two slit sides.

preprint2012arXivOpen access
Dmitri Prokhorov
math.CV
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Dmitri Prokhorov

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