Mathematics Graduate Students Organization

Seminar:

Date: March 11

Although convexity is not preserved under holomorphic changes of coordinates, the Riemann mapping theorem provides us with a means to characterize which planar domains are equivalent to convex ones. Unfortunately, this theorem does not immediately generalize to higher dimensions. Recently, there has been some work done to characterize those domains that are equivalent to convex domains. I will discuss some of the history of this problem and recent results about the images of various ${\scriptstyle l^p}$ balls under the symmetrization map, ${\scriptscriptstyle(z_1,z_2)\to(z_1+z_2,z_1z_2)}$.