Global solutions and asymptotics of Teichm\"uller harmonic map flow

Melanie Rupflin (Leipzig)

Teichm\"uller harmonic map flow is a gradient flow of the Dirichlet
energy which is designed to evolve parametrised surfaces towards
critical points of the Area. 

In this talk we will discuss some new results for this flow and show in
particular that for non-positively curved targets the flow changes or
decomposes arbitrary closed initial surfaces into minimal immersions
(possibly with branch points) through globally defined smooth solutions.