Monday Analysis Seminar: Geometry of metric spaces via weighted partitions by trees

2016-11-15 16:30 - 2016-11-15 18:00
Faculty of Science Buliding #3 Room 210
Jun Kigami (Kyoto University)
We are going to consider successive division of a space like the binary division of the unit interval. The notion of successive division of a space has been appeared in many area of mathematics. For example, self-similar sets are divided into pieces which are similar to the original set by means of the contractions characterizing the self-similar set itself. Moreover, in dynamical systems, Markov partition associated with a hyperbolic dynamical systems is one of the standard tool of the study. In harmonic analysis, there is the notion of dyadic cubes associated with a measure with the volume doubling property. In this talk, we will introduce weighs of the pieces of the successive division of a metric space and study the associated geometry of the set. In this way, we may unify the notions of metrics and measures. For example, we will show that the notion of quasisymmetry between metrics and the notion of the volume doubling property between a metric and a measure is the same in this point of view.

Different day of the week.