Regularity of Loewner Curves

Joan Lind; Huy Tran

Regularity of Loewner Curves

Complex Variables 2014-11-11 v1

Authors: Joan Lind , Huy Tran

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.

Keywords

algebraic curves random matrix ensembles

Cite

@article{arxiv.1411.2164,
  title  = {Regularity of Loewner Curves},
  author = {Joan Lind and Huy Tran},
  journal= {arXiv preprint arXiv:1411.2164},
  year   = {2014}
}

Comments

32 pages, 5 figures

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