Speaker: Dimitrios Ntalampekos, assistant professor, Stony Brook University, New York

Date: October 9, 2023

Time: 20:00-21:00

Location: Zoom

Sponsor: Frontiers Science Center for Nonlinear Expectations, Shandong University; Research Centre for Mathematics and Interdisciplinary Sciences Centre, Shandong University; Sino-Russian Mathematics Center in Qingdao

Abstract:

The classical uniformization theorem for Riemann surfaces implies that every smooth two-dimensional sphere can be conformally parametrized by the Euclidean sphere. The recent developments in the field of Analysis on Metric Spaces have allowed the extension of this result beyond the smooth setting. Sufficient geometric conditions have been established so that a fractal sphere can be transformed to the Euclidean sphere with a bi-Lipschitz, quasisymmetric, or quasiconformal map. The milestones in this direction are the works of Bonk-Kleiner on the quasisymmetric uniformization of spheres and of Rajala on the characterization of quasiconformal spheres. It was conjectured by Rajala and Wenger that, under no assumption, every metric two-dimensional sphere of finite area can be parametrized by the Euclidean sphere with a weakly quasiconformal map. In this talk we present an affirmative answer to this conjecture.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/184019.htm