147 citations · 365 across the 33 of their papers we have counts for
4 papers · 1 filter
A uniform Poincaré estimate for quadratic differentials on closed surfaces
Melanie Rupflin, Peter M. Topping
We prove a uniform estimate, valid for every closed Riemann surface of genus at least two, that bounds the distance of any quadratic differential to the finite dimensional space of…
Asymptotics of the Teichmüller harmonic map flow
Melanie Rupflin, Peter M. Topping, Miaomiao Zhu
The Teichmüller harmonic map flow, introduced in [9], evolves both a map from a closed Riemann surface to an arbitrary compact Riemannian manifold, and a constant curvature metric…
Flowing maps to minimal surfaces: Existence and uniqueness of solutions
Melanie Rupflin
We study the new geometric flow that was introduced in [11] that evolves a pair of map and (domain) metric in such a way that it changes appropriate initial data into branched mini…
Flowing maps to minimal surfaces
Melanie Rupflin, Peter M. Topping
We introduce a flow of maps from a compact surface of arbitrary genus to an arbitrary Riemannian manifold which has elements in common with both the harmonic map flow and the mean…