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arXiv · 1707.01023

Loewner Equation driven by complex-valued functions

Huy Tran
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Abstract

Consider the Loewner equation associated to the upper-half plane. Normally this equation is driven by a real-valued function. In this paper, we show that when the driving function is complex-valued with small $1/2$-Hölder norm, the corresponding hull is a quasi-arc, hence is a simple curve. We also study how the hull changes with respect to complex parameters and make a connection between Loewner equation and complex dynamics.

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Huy Tran. 2017-07-04. Loewner Equation driven by complex-valued functions. https://arxiv.org/abs/1707.01023

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