The Loewner driving function of trajectory arcs of quadratic differentials

被引：6

作者：

Tsai, J. ^{[1
]}

机构：

[1] Chinese Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 360卷 / 02期

关键词：

Loewner differential equation; Driving function; Quadratic differential; EQUATION;

D O I：

10.1016/j.jmaa.2009.07.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain a first order differential equation for the driving function of the chordal Loewner differential equation in the case where the domain is slit by a curve which is a trajectory arc of a certain type of quadratic differential. In particular this includes the case when the curve is a path on the square, triangle or hexagonal lattice in the upper half-plane or, indeed, in any domain with boundary on. the lattice. We also demonstrate how we use this to calculate the driving function numerically. Equivalent results for other variants of the Loewner differential equation are also obtained. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：561 / 576

页数：16

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