6 papers · 1 filter
Uniqueness and nonuniqueness of limits of Teichmueller harmonic map flow
James Kohout, Melanie Rupflin, Peter M. Topping
The harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consi…
Finite-time degeneration for variants of Teichmüller harmonic map flow
Craig Robertson, Melanie Rupflin
We consider the question of whether solutions of variants of Teichmüller harmonic map flow from surfaces to general targets can degenerate in finite time. For the original flow…
Hyperbolic metrics on surfaces with boundary
Melanie Rupflin
We discuss an alternative approach to the uniformisation problem on surfaces with boundary by representing conformal structures on surfaces of general type by hyperbolic metric…
Holomorphic quadratic differentials dual to Fenchel-Nielsen coordinates
Nadine Große, Melanie Rupflin
We discuss bases of the space of holomorphic quadratic differentials that are dual to the differentials of Fenchel-Nielsen coordinates and hence appear naturally when considering f…
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…