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.
Duke Math. J.
154(3):
527-573
(15 September 2010).
DOI: 10.1215/00127094-2010-045
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