Alex Austin : The Quasiconformal Jacobian Problem

Posted by Xudong Zheng , part of the Graduate Student Colloquium.

At

Feb. 13, 2014, 4 p.m.

In

SEO 636

Abstract

If two metric spaces are bi-Lipschitz equivalent, then they are effectively the same. Using the fundamental question, 'When is a metric space bi-Lipschitz equivalent to the Euclidean space $\mathbb{R}^n$?', as motivation, I will introduce the (still far from solved) quasiconformal Jacobian problem: characterize those weights on $\mathbb{R}^n$ comparable to the Jacobian of a quasiconformal map. I will discuss a result of Bonk, Heinonen and Saksman which displays a class of weights which are comparable to quasiconformal Jacobians, and a result of Kovalev and Maldonado which gives information on how wide to cast your net if you seek a characterization.

Pizza will be served.