Minkowski容量参数化下SLE8的Holder连续性  

The Holder continuity of SLE8 under Minkowski capacity parameterization

作　　者：梁静 LIANG Jing(School of Finance and Mathematics,Huainan Normal University,Huainan 232001,China)

机构地区：[1]淮南师范学院金融与数学学院,安徽淮南232001

出　　处：《延边大学学报（自然科学版）》2024年第3期1-6,共6页Journal of Yanbian University（Natural Science Edition）

基　　金：安徽省质量工程项目(2023jcjx021);安徽省质量工程项目(2022cxtd141)。

摘　　要：在已知κ∈(0,4]时,SLE_(κ)曲线η不是局部d/1−Holder连续基础之上,研究了SLE8的Holder连续性问题.通过运用Koebe失真定理和Radon-Nikodym导数,分析将双边全平面SLE_(κ)的曲线η(在d维Minkowski容量参数下)转变为指数为d 1的带有固定增量的自我相似过程.同时,证明了带有固定增量的自我相似SLE8曲线η,在任意开区间上都不是d/1−Holder连续的,即SLE8曲线η在任意开区间上不是d/1−Holder连续的.研究结果可为SLE8的Holder连续性研究提供参考.The Holder continuity problem of SLE8 is studied.Firstly,based on the SLE_(κ)curveηis not locally d/1−Holder continuous forκ∈(0,4],then the distortion theorem and Radon-Nikodym derivative are used to transform the two-sided full-plane SLE_(κ)curveηinto an exponential self-similar process with a fixed increment d/1 under Minkowski capacity parameter.Secondly,the self-similar SLE8 curveηwith fixed increments are not d/1−Holder continuous on any open interval,that is,the SLE8 curveηis not d/1−Holder continuous on any open interval.The results can provide a reference for the Holder continuity of SLE_(κ).

关 键 词：Minkowski容量 参数化 HOLDER连续 停时 

分 类 号：O177.1[理学—数学] O152.21[理学—基础数学]