Hyperbolic graphs induced by weighted iterated function systems

报告人：孔诗磊（德国比勒菲尔德大学）

报告地点：工商楼200-9

报告时间：12月9日上午10点半—11点半

摘要：For an iterated function system (IFS) $\{S_j\}_{j=1}^N$ of contractive similitudes on $\mathbb{R}^d$, there is a well-known graph structure (augmented tree) X, which is (Gromov-)hyperbolic under the open set condition or some other circumstances. In this talk, we study the hyperbolicity of a new graph $X(s)$ induced by an IFS $\{S_j\}_{j=1}^N$ and a weight $s\in (0, 1)^N$. For the cases that the hyperbolicity holds, we also investigate the relation of the induced Gromov metric and the self-similar measure. In particular, if the IFS $\{S_j\}_{j=1}^N$ is post critically finite (p.c.f.) and admits a regular harmonic structure with weight $s$, we prove that the hyperbolic boundary of $X(s)$ is H\{o}lder equivalent to the self-similar set equipped with the resistance metric. This is a joint work with Ka-Sing Lau and Xiang-Yang Wang.

联系人：阮火军老师ruanhj@zju.edu.cn