22 citations · 52 across the 20 of their papers we have counts for
26 papers
Flowing to free boundary minimal surfaces
Melanie Rupflin, Michael Struwe, Christopher Wright
We introduce a flow that is designed to flow maps which map the boundary of a general domain surface into a given (not necessarily connected) submanifold…
A sharp quantitative stability result near infinitely concentrated minimisers
Melanie Rupflin, Sebastian Woodward
We consider the question of quantitative stability of minimisers for a well-known variational problem for which the infimum of the energy is not achieved in the classical sense, na…
Quantitative estimates for the relative isoperimetric problem and its gradient flow outside convex bodies in the plane
Elena Mäder-Baumdicker, Robin Neumayer, Jiewon Park +1
We prove three related quantitative results for the relative isoperimetric problem outside a convex body in the plane: (1) Łojasiewicz estimates and quantitative rigidity for c…
Sharp quantitative rigidity results for maps from to of general degree
Melanie Rupflin
As the energy of any map from to is at least with equality if and only if is a rational map one might ask whether maps with small energy d…
Low energy levels of harmonic maps into analytic manifolds
Melanie Rupflin
We consider the energy spectrum of harmonic maps from the sphere into a closed Riemannian manifold . While a well known conjecture asserts that is discrete whe…
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…
Lojasiewicz inequalities for almost harmonic maps near simple bubble trees
Melanie Rupflin
We prove Lojasiewicz inequalities for the harmonic map energy for maps from surfaces of positive genus into general analytic target manifolds which are close to simple bubble trees…
Łojasiewicz inequalities near simple bubble trees
Andrea Malchiodi, Melanie Rupflin, Ben Sharp
In this paper we prove a gap phenomenon for critical points of the -functional on closed non-spherical surfaces when is constant, and in this setting furthermore prove that…
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…
Global weak solutions of the Teichmüller harmonic map flow into general targets
Melanie Rupflin, Peter M. Topping
We analyse finite-time singularities of the Teichmüller harmonic map flow -- a natural gradient flow of the harmonic map energy -- and find a canonical way of flowing beyond them i…
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…
Sharp eigenvalue estimates on degenerating surfaces
Nadine Große, Melanie Rupflin
We consider the first non-zero eigenvalue of the Laplacian on hyperbolic surfaces for which one disconnecting collar degenerates and prove that essentiall…
Horizontal curves of hyperbolic metrics
Melanie Rupflin, Peter M. Topping
We analyse the fine convergence properties of one parameter families of hyperbolic metrics, on a fixed underlying surface, that move always in a horizontal direction, i.e. orthogon…
Smooth long-time existence of Harmonic Ricci Flow on surfaces
Reto Buzano, Melanie Rupflin
We prove that at a finite singular time for the Harmonic Ricci Flow on a surface of positive genus both the energy density of the map component and the curvature of the domain mani…
Refined asymptotics of the Teichmüller harmonic map flow into general targets
Tobias Huxol, Melanie Rupflin, Peter M. Topping
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, wher…
Teichmüller harmonic map flow from cylinders
Melanie Rupflin
We define a geometric flow that is designed to change surfaces of cylindrical type spanning two disjoint boundary curves into solutions of the Douglas-Plateau problem of finding mi…
Weak solutions to mean curvature flow respecting obstacles I: the graphical case
Melanie Rupflin, Oliver C. Schnürer
We consider the problem of evolving hypersurfaces by mean curvature flow in the presence of obstacles, that is domains which the flow is not allowed to enter. In this paper, we tre…
Teichmüller harmonic map flow into nonpositively curved targets
Melanie Rupflin, Peter M. Topping
The Teichmüller harmonic map flow deforms both a map from an oriented closed surface into an arbitrary closed Riemannian manifold, and a constant curvature metric on , so as…
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…