Local Analysis of Loewner Equation

2018/04/10 by Henshui Zhang, Zhang, Henshui, Zinsmeister, Michel
Mathematics · #30C20 #30C62 #30E25 #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1804.03410

openalex publication_date 2018/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let λ:[0,+∞)↦ℝ be the driving function of a chordal Loewner process. In this paper we find new conditions on λ which imply that the process is generated by a simple curve. This result improves former one by Lind ,Marshall and Rhode, and it particular gives new results about the case λ(t)=cW_b(t), W_b being a Hölder-1/2 Weierstrass function. In the second part we find new conditions on λ implying that the process is generated by a curve. The main tool here is a duality relation between the real part and the imaginary part of the Loewner equation.

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