Smoothness of Loewner slits

Wong, Carto

doi:10.1090/S0002-9947-2013-05873-4

Smoothness of Loewner slits
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Trans. Amer. Math. Soc. 366 (2014), 1475-1496 Request permission

Abstract:

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

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