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| The properties of SLE hull in the strip region |
| TIAN Shuang-shuang, LAN Shi-yi |
| School of science, Guangxi University for Nationalities, Nanning 530006, China |
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Abstract In this paper, the properties of SLE hull in the strip region are discussed by using the properties of strip SLE and Schwarz reflection principe. The relation between $\mathbb{R}$-symmetric conformal mappings and hulls in the strip region is given. The relationship between the set which consists of a pair of disjoint hulls and Loewner conformal mappings is obtained. It is derived that the lift of a $\mathbb{R}$-symmetric conformal mapping is continuous in the space of hulls in the strip region, and that some related mappings are continuous in the corresponding space of hulls, too. This generalizes the related properties of SLE hull in the upper half-plane to the case of strip region.
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Received: 16 January 2016
Published: 16 May 2018
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带形区域上SLE壳的性质
利用带形区域上SLE的性质与Schwarz反射原理, 讨论了带形区域上SLE壳的性质. 给出了$\mathbb{R}$-对称共形映射与带形区域内壳的关系; 得到了带形区域内由一对不相交的壳组成集合与Loewner共形映射之间的关系; 导出了$\mathbb{R}$-对称共形映射的提升在带形区域的壳空间内以及带形区域的壳对空间上的相关映射是连续. 这就将上半平面上SLE壳的有关性质推广到了带形区域的情形.
关键词：
Loewner方程,
SLE,
壳,
共形映射
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