An Aronsson type approach to extremal quasiconformal mappings.

Monday, May 16, 2011 - 4:00pm - 4:30pm
Lind 305
Luca Capogna (University of Arkansas)
Quasiconformal mappings u:Ω->Ω between open
domains in Rn, are W{1,n} homeomorphisms whose dilation K=du/
(det du)1/n is in L∞. 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 C2 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.
MSC Code: