Exponential driving function for the Löwner equation
arXiv:1201.0886
Abstract
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 -curve. We give an asymptotic estimate for the ratio of harmonic measures of the two slit sides.