Driving function of the vertical slit

Abstract

We consider the chordal Loewner equation and construct a family of vertical slits ?p (p > 0). We give the exact expression of its driving function ?, and its H?lder 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 ? to a general case.