Quasiconformal geometry and the boundary of hyperbolic groups
发布时间：2023年03月13日
浏览次数：2786
发布者: Biao Ma
主讲人： 李文博（BICMR）
活动时间： 从 2023-03-20 15:00 到 16:30
场地： 北京国际数学研究中心，全斋全29教室
Abstract:A Hyperbolic space is a metric space whose geodesic triangles are "thin" and a hyperbolic group is a group whose Cayley graph is hyperbolic. We focus on the boundary of hyperbolic groups in this talk and go through topics around two rigidity conjectures: The Cannon Conjecture and the Kapovich-Kleiner Conjecture. Roughly speaking, these two conjectures ask about whether special topological restrictions on the boundary of hyperbolic groups will uniquely determine them up to quasisymmetries. In an effort to answer these questions, many people have studied them from different approaches. We will go through the work by Bonk and Kleiner. In the end, we provide our trying on these conjectures. In particular, we have constructed a special case of metric Sierpinski carpet, dyadic slit carpets, and completely characterize its planar quasisymmetric embeddability.
