7 papers
Global minimality of the Hopf map in the Faddeev-Skyrme model with large coupling constant
André Guerra, Xavier Lamy, Konstantinos Zemas
We prove that, modulo rigid motions, the Hopf map is the unique minimizer of the Faddeev--Skyrme energy in its homotopy class, provided that the radius of the target 2-sphere is no…
Constraint Maps: Insights and Related Themes
Alessio Figalli, André Guerra, Sunghan Kim +1
This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intric…
Constraint maps and free boundaries
Alessio Figalli, André Guerra, Sunghan Kim +1
In this short expository note, we present a selection of classic and recent ideas in free boundary theory, with a focus on the vectorial case, referred to here as constraint maps.…
On the existence of degenerate solutions of the two-dimensional -system
André Guerra, Xavier Lamy, Konstantinos Zemas
We consider entire solutions of the -system which we refer to as bubbles. Surprisingly, and contrary to conjectures r…
Constraint maps: singularities vs free boundaries
Alessio Figalli, André Guerra, Sunghan Kim +1
Energy-minimizing constraint maps are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, these maps manifest a diver…
Optimal quantitative stability of the Möbius group of the sphere in all dimensions
André Guerra, Xavier Lamy, Konstantinos Zemas
In any dimension , we prove an optimal stability estimate for the Möbius group among maps , of the form $\inf_{λ>0,ϕ\in \mathrm{Mö…
Constraint maps with free boundaries: the Bernoulli case
Alessio Figalli, André Guerra, Sunghan Kim +1
In this manuscript, we delve into the study of maps that minimize the Alt-Caffarelli energy functional u…