## 月曜解析セミナー： Geometry of domains and maps

2017年 　 8月 7日 13時 30分 ～ 2017年 　 8月 7日 15時 00分

Matti Vuorinen (University of Turku, Finland)

My talk will deal with the study of geometric properties of domains in $\mathbb{R}^n$ and quasiconformal maps defined on them. An important idea in this work is the study of how distances are changed under maps. The variation of geometric and topological properties of balls with a fixed center and varying radius reflects the nature of the boundary of the domain. Metrics can be defined in many ways, e.g. in terms of capacity, angles or distances and each geometry has different balls. We also employ the number of Whitney cubes of a given generation for this purpose. Mostly I will discuss results from my joint papers in arXiv during the past five years.