Driving function of the vertical slit

Hai-Hua Wu

We consider the chordal Loewner equation and construct a family of vertical slits γ p (p > 0). We give the exact expression of its driving function λ, and its H ¨ older exponent near 0 in terms of p, which maps onto (1/2, ∞) and has a natural connection with the known results. In addition, we extend the asymptotic behavior of the driving function λ to a general case.