报告人：阮火军（浙江大学）

时间：2022年06月08日10:00开始

腾讯会议ID：411 158 310（无密码）

摘要：We investigate a class of self-similar sets called generalized Sierpinski carpets (or shortly GSCs). It follows from two well-known results by Hata and Whyburn that a connected GSC is homeomorphic to the standard Sierpinski carpet if and only if it has no local cut points. On the one hand, we show that to determine whether a given GSC is connected, it suffices to iterate the initial pattern twice. On the other hand, we obtain two criterions: (1) for a connected GSC to have cut points, (2) for a connected GSC with no cut point to have local cut points. With these two criteria, we characterize all GSCs that are homeomorphic to the standard Sierpinski carpet.

 Our results hold for Baranski carpets. Moreover, we extend the connectedness result to Baranski sponges.This is a joint work with Xin-Rong Dai, Jun Luo, Yang Wang and Jian-Ci Xiao.

简介：阮火军，浙江大学数学科学学院教授，2000年博士毕业于浙江大学，2000年至2002年在南京大学进行博士后工作，2002年开始在浙江大学任教，其中，2007年至2009年在美国Cornell大学访问。研究领域为分形几何，主要方向包括：分形集的Lipschitz等价性；分形上的分析；分形插值函数。

邀请人：罗军

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