报告人：Antti Rasila 研究员（Aalto University）

报告时间：5月7日下午3点

报告地点：数学实验室

报告摘要:
We discuss the quasihyperbolic metric and the concept of (dimension) free quasiconformality,which was introduced by J. Väisälä as a tool for generalizing the theory of quasiconformal mappings of n-dimensional Euclidean spaces into infinite dimensional Banach spaces. This concept relies heavily on the quasihyperbolic metric.In this presentation, we give an historical overview to the theory and outline some recent advances in the study of the quasihyperbolic metric. Furthermore, we establish results demonstrating that this concept is useful in a very general metric setting. First, we show several sufficient conditions for a homeomorphism to be fully semisolid in suitable metric spaces. These onditions indicate that the quasihyperbolic metrics are quasi-invariant under several different kinds of mappings, for example, quasisymmetric mappings, weakly quasisymmetric mappings.