Time: 14:00-15:00, Wednesday, October 16 2024
Venue: E4-233, Yungu Campus
Host: Thierry De Pauw, ITS
Speaker: Hui Rao, Central China Normal University
Biography: Professor Hui Rao obtained his bachelor degree from Sichuan University and his master and doctoral degrees from Wuhan University. He held positions at many institutions including Wuhan University, Tsinghua University, Nanjing University, The Chinese University of Hong-Kong, and Tsuda College. He is now a Professor at Central China Normal University. His work is on fractal geometry, tiling theory, and symbolic dynamic system.
Title: Box-counting measures of metric spaces
Abstract: In a metric space (X, d), a measure μ is called an Ahlfors regular measure if the measure of any ball with radius r is proportional to rs for some constant s. Ahlfors regular measure plays an important role in analysis of metric spaces. We introduce a notion of box-counting measure, where μ(A) measures the number of δ-boxes intersecting a set A. Indeed, this measure is a generalization of Ahlfors regular measure. For general self-affine sets, there exist box-counting measures but there does not exist Ahlfors measure. First, we show that the multi-fractal spectrum of a box-counting measure is a Lipschitz invariant. Secondly, we show that any bi Lipschitz map between two metric spaces with box-counting measures are (locally) measure preserving.
