Regularity of Loewner Curves

Joan Lind; Huy Tran

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arXiv · 1411.2164

Regularity of Loewner Curves

Joan Lind·Huy Tran

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Abstract

The Loewner equation encrypts a growing simple curve in the plane into a real-valued driving function. We show that if the driving function $\lambda$ is in $C^{\beta}$ with $\beta>2$ (or real analytic) then the Loewner curve is in $C^{\beta + \frac{1}{2}}$ (respectively analytic). This is a converse to a result by Earle and Epstein and extends a result of Wong.

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Joan Lind, Huy Tran. 2014-11-08. Regularity of Loewner Curves. https://arxiv.org/abs/1411.2164

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