The Properties Of Dipolar SLEs In Multiply Connected Domains

Stochastic Loewner evolution(SLE for short)is a family of random planar growth processes with one-parameter,which can be described by a solution of a Loewner differential equation with the driving term being a time-change of one-dimensional Brownian motion.For the study of SLE,SLEs in simply connected domains are generalized to multiply connected domains.The main work of this thesis is as follows: First,we derive expressions of Komatu-Loewner equation for dipolar SLE and slit differential equations in multiply connected domains;Secondly,we discuss the properties of trace and the driving function for dipolar SLE in multiply connected domains;Finally,we show that dipolar SLEs in multiply connected domains enjoy scaling property and locality property.