Seminar

The Grushin plane can be thought of as a two-dimensional Euclidean plane with a metric that “blows up” near the vertical axis. This gives the vertical axis a Hausdorff dimension of two. We begin by introducing the Grushin plane and discuss some basic properties. Then, we discuss a counterexample to show how analysis on the Grushin plane differs from Euclidean analysis. After that, we construct a quasiconformal map from the Grushin plane to the Euclidean plane. We finish by generalizing the Grushin plane slightly and explaining how the Grushin plane can serve as an intermediary in dealing with quasiconformal maps on Euclidean spaces.