3 citations · 3 across the 8 of their papers we have counts for
9 papers
Integral curvature estimates and geodesic limits for stable abelian Higgs fields
Marco Badran, Marco A. M. Guaraco, Aria Halavati
We prove that, on closed three-manifolds, the limit interface of a sequence of stable abelian Higgs critical points with uniformly bounded energy is a finite union of smooth closed…
Stable solutions in the abelian Higgs model
Marco Badran
We classify entire stable solutions with quadratic energy growth in the -dimensional abelian Higgs model. More precisely, we prove that such solutions are holomorphic with respe…
A two-dimensional Allen-Cahn theory for interfaces with boundary
Marco Badran, Manuel del Pino, Marco A. M. Guaraco
We develop a two-dimensional Allen-Cahn theory for interfaces with boundary in the line-bundle framework introduced by Fröhlich and Struwe. The central new object is a model soluti…
Uniform small energy regularity for fractional geometric problems
Marco Badran, Giacomo Cozzi
We prove small energy regularity for a parabolic boundary reaction Ginzburg-Landau problem in the full range , answering a question posed by Hyder, Segatti, Sire and Wa…
Nonlocal free boundary minimal surfaces
Marco Badran, Serena Dipierro, Enrico Valdinoci
We introduce the nonlocal analogue of the classical free boundary minimal hypersurfaces in an open domain of as the (boundaries of) critical points of the fracti…
Stationary -harmonic maps approaching planar singular harmonic maps to the circle
Marco Badran, Jean Van Schaftingen
Given a bounded planar domain , we show that any singular harmonic map into the circle corresponding to a topologically nondegenerate critical…
Harmonic maps to the circle with higher dimensional singular set
Marco Badran
In a closed, oriented ambient manifold we consider the problem of finding -valued harmonic maps with prescribed singular set. We show that the boundary of a…
Solutions of the Ginzburg-Landau equations concentrating on codimension-2 minimal submanifolds
Marco Badran, Manuel del Pino
We consider the magnetic Ginzburg-Landau equations in a compact manifold $$ \begin{cases} -\varepsilon^2 Δ^{A} u=\frac{1}{2}(1-|u|^2)u,\\ \varepsilon^2 d^*dA=\langle\nabla^A u,…
Entire solutions to 4-dimensional Ginzburg-Landau equations and codimension 2 minimal submanifolds
Marco Badran, Manuel del Pino
We consider the magnetic Ginzburg-Landau equations in $$ \begin{cases} -\varepsilon^2(\nabla-iA)^2u = \frac{1}{2}(1-|u|^{2})u,\\ \varepsilon^2 d^*dA = \langle(\nabla…