Smoothness of Loewner Slits

Abstract

In this paper, we show that the chordal Loewner differential equation with $C^{\beta }$ driving function generates a $C^{\beta +1/2}$ slit for $1/2<\beta \le 2$, except when $\beta =3/2$ the slit is only proved to be weakly $C^{1,1}$.

30 pages, 6 figures

References in corpus (1)

• A Sharp Condition for the Loewner Equation to Generate Slits