發(fā)布時(shí)間：2018-05-23 17:11

  本文選題：SLE_κ + 殼��； 參考：《廣西民族大學(xué)》2016年碩士論文

【摘要】：隨機(jī)Loewner演變(簡(jiǎn)稱(chēng)SLE或SLE_κ)是通過(guò)解驅(qū)動(dòng)函數(shù)為時(shí)間改變的布朗運(yùn)動(dòng)的Loewner微分方程來(lái)描述的一類(lèi)帶有一個(gè)參數(shù)κ的共形不變隨機(jī)分形曲線(xiàn)族.對(duì)SLE_κ的研究,從上半平面和單位圓盤(pán)上的典型SLE_κ被推廣到一般區(qū)域的情形.本文的主要工作如下:第一,討論了帶形區(qū)域上SLE_κ殼的性質(zhì).利用帶形區(qū)域上SLE_κ的性質(zhì)與Schwarz反射原理,給出了R-對(duì)稱(chēng)共形映射與帶形區(qū)域內(nèi)殼的關(guān)系;得到了帶形區(qū)域內(nèi)由一對(duì)不相交的殼組成集合與Loewner共形映射之間的關(guān)系;導(dǎo)出了R-對(duì)稱(chēng)共形映射的提升在帶形區(qū)域的殼空間內(nèi)以及帶形區(qū)域的殼對(duì)空間上的相關(guān)映射是連續(xù)的.這就將上半平面上SLE殼的有關(guān)性質(zhì)推廣到了帶形區(qū)域的情形.第二,研究了帶形區(qū)域上反向SLE_κ的性質(zhì).應(yīng)用Leowner方程定義帶形區(qū)域上反向SLE_κ、向前Loewner鏈和反向Loewner鏈;討論了帶形區(qū)域上向前Loewner鏈和反向Loewner鏈的性質(zhì),得到了向前Loewner殼與向前Loewner鏈之間以及反向Loewner殼和反向Loewner鏈之間的關(guān)系;討論了涉及一些簡(jiǎn)單曲線(xiàn)的隨機(jī)共形粘合.
[Abstract]:Stochastic Loewner evolution (SLE or SLEK) is a class of conformal invariant random fractal curves with a parameter 魏, which is described by solving the Loewner differential equation of Brownian motion with time-varying driving function. The study of SLEK is extended from the typical SLE- 魏 on the upper half plane and the unit disk to the general domain. The main work of this paper is as follows: first, we discuss the properties of SLE- 魏 shells in the zonal region. By using the properties of SLE- 魏 and the Schwarz reflection principle, the relation between the R- symmetric conformal mapping and the inner shell of the band region is given, and the relation between the Loewner conformal mapping and the set of disjoint shells in the zonal region is obtained. It is derived that the lifting of R- symmetric conformal mapping is continuous in the shell space of the band region and the correlation mapping between the shell and the space of the belt region. This extends the properties of the SLE shell on the upper half plane to the case of a zonal region. Secondly, we study the properties of reverse SLE- 魏 in the zonal region. The Leowner equation is used to define the reverse SLE- 魏, forward Loewner chain and reverse Loewner chain in the band region, and the properties of the forward Loewner chain and reverse Loewner chain in the band region are discussed, and the relations between the forward Loewner shell and the forward Loewner chain, as well as the reverse Loewner shell and the reverse Loewner chain are obtained. Random conformal bonding involving some simple curves is discussed.
【學(xué)位授予單位】：廣西民族大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：O211.6

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