22 citations · 52 across the 20 of their papers we have counts for
11 papers · 1 filter
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…
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…
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…
Selfsimilar expanders of the harmonic map flow
Pierre Germain, Melanie Rupflin
We study the existence, uniqueness, and stability of self-similar expanders of the harmonic map heat flow in equivariant settings. We show that there exist selfsimilar solutions to…