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A Sharp Condition for the Loewner Equation to Generate Slits

Joan R. Lind

math.CVarXiv:math/0311234

Abstract

D. Marshall and S. Rohde have recently shown that there exists C0 >0 so that the Loewner equation generates slits whenever the driving term is Hölder continuous with exponent 1/2 and norm less than C0. In this paper, we show that the maximal value for C0 is 4.

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