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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
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