Event Date
2011-05-02
Event Time
02:30 pm ~ 03:03 pm
Event Location
Wachman 617
Abstract: Quasiconformal mappings $u:\Omega\to\Omega'$ between open domains in $\mathbb{R}^{n}$, are $W^{1,n}$ homeomorphisms whose dilation $K = |du|/(\det du)^{1/n}$ is in $L^{\infty}$. A classical problem in geometric function theory consists in finding QC minimizers for the dilation within a given homotopy class or with prescribed boundary data. In a joint work with A. Raich we study $C^{2}$ extremal quasiconformal mappings in space and establish necessary and sufficient conditions for a ‘localized’ form of extremality in the spirit of the work of G. Aronsson on absolutely minimizing Lipschitz extensions. We also prove short time existence for smooth solutions of a gradient flow of QC diffeomorphisms associated to the extremal problem.