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A Sharp Condition for the Loewner Equation to Generate Slits

Joan R. Lind
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Abstract

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 1/2 and norm less than $C_0$. In this paper, we show that the maximal value for $C_0$ is 4.

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Joan R. Lind. 2003-11-14. A Sharp Condition for the Loewner Equation to Generate Slits. https://arxiv.org/abs/math/0311234

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