A sharp condition for the Loewner equation to generate slits. (English) Zbl 1069.30012
Summary: D. Marshall and S. Rohde have recently shown that there exists \(C_0>0\) so that the Loewner equation generates slits whenever the driving term is Hölder continuous with exponent \(\frac 12\) and norm less than \(C_0\). In this paper, we show that the maximal value for \(C_0\) is 4.
MSC:
30C35 | General theory of conformal mappings |