Global solutions and Asymptotics of Teichmüller harmonic map flow
Vortrag von Dr. Melanie Rupflin
Datum: 12.11.13 Zeit: 15.00 - 17.00 Raum: ETH
Teichmüller harmonic map flow is designed to evolve maps from a closed surface to a general target manifold towards branched minimal immersions. Defined as gradient flow of energy considered as a function of both a map and a metric on the domain, the flow enjoys the strong regularity properties known from harmonic map heat flow for as long as there is no degeneration in Teichmüller space. In this talk we will discuss the asymptotic behaviour of global solutions of the flow, guaranteed to exist in certain settings, and prove that any global solution changes (or decomposes) the initial data into (a union of) branched minimal immersions, possibly parametrized over surfaces of lower genus. This is joint work with Peter Topping.