Exponential driving function for the L\"owner equation
Abstract
We consider the chordal L\"owner differential equation with the model driving function 3 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 L\"owner equation map slit domains onto the upper half-plane. The slit is a C1-curve. We give an asymptotic estimate for the ratio of harmonic measures of the two slit sides.
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