Collisions and Spirals of Loewner Traces
Collisions and Spirals of Loewner Traces
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DOI：
10.1215/00127094-2010-045
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发表时间：
2009-01
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影响因子：
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通讯作者：
Joan R. Lind;D. Marshall;S. Rohde
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文献类型：
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作者：
Joan R. Lind;D. Marshall;S. Rohde
我们分析了由渐近于K \sqrt{1-t}的函数驱动的Loewner轨迹。我们证明了K不为4时的稳定性结果，并表明K=4会导致非局部连通船体。因此，我们得到一个驱动项\lambda (t)，使得K驱动的船体\lambda (t)是由K不等于4但K不等于4时所有K > 0的连续曲线生成的，因此具有连续轨迹的驱动项空间不是凸的。作为一个副产品，我们得到了K \sqrt{1-t}驱动的轨迹的显式构造和Kager， Nienhuis和Kadanoff的相应结果的概念证明，math-ph/0309006
We analyze Loewner traces driven by functions asymptotic to K\sqrt{1-t}. We prove a stability result when K is not 4 and show that K=4 can lead to non locally connected hulls. As a consequence, we obtain a driving term \lambda(t) so that the hulls driven by K\lambda(t) are generated by a continuous curve for all K > 0 with K not equal to 4 but not when K = 4, 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 K\sqrt{1-t} and a conceptual proof of the corresponding results of Kager, Nienhuis and Kadanoff, math-ph/0309006