Abstract
We analyze Loewner traces driven by functions asymptotic to . We prove a stability result when , and we show that can lead to nonlocally connected hulls. As a consequence, we obtain a driving term so that the hulls driven by are generated by a continuous curve for all with , but not when , so that the space of driving terms with continuous traces is not convex. As a byproduct, we obtain an explicit construction of the traces driven by and a conceptual proof of the corresponding results of Kager, Nienhuis, and Kadanoff.
Citation
Joan Lind. Donald E. Marshall. Steffen Rohde. "Collisions and spirals of Loewner traces." Duke Math. J. 154 (3) 527 - 573, 15 September 2010. https://doi.org/10.1215/00127094-2010-045
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