Diff. Geom, Math. Phys., PDE Seminar: Tobias Huxol

The Teichmüller harmonic map flow is a gradient flow for the harmonic map energy of maps from a closed surface to a general closed Riemannian target manifold of any dimension, where both the map and the domain metric are allowed to evolve. It was introduced by M. Rupflin and P. Topping in 2012. The objective of the flow is to find branched minimal immersions on a given surface. We will give some background on the flow and then describe some recent work. In particular we show that if the flow exists for all times then in a certain sense the maps (sub-)converge to a collection of branched minimal immersions with no loss of energy (even when allowing for degeneration of the metric at infinity). We also construct an example of a smooth flow where the image of the limit maps is disconnected. This is joint work with M. Rupflin and P. Topping.