8 papers
Convergence of almost harmonic maps to geodesic bubble trees
Melanie Rupflin
We prove a sharp criterion on the decay of the tension of almost harmonic maps from degenerating surfaces that ensures that such maps subconverge to a limiting object that is made…
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…
Analysis of boundary bubbles for almost minimal cylinders
Melanie Rupflin, Matthew R. I. Schrecker
We analyse the asymptotic behaviour of solutions of the Teichmüller harmonic map flow from cylinders, and more generally of `almost minimal cylinders', in situations where the maps…