Xavier Lamy

activity

20232026

collaborators

10 papers

math.AP2026

Some lifting and approximation properties for maps in $W^{1, 2} (B^{3}; S^{2})$

André Guerra, Xavier Lamy, Konstantinos Zemas

Smooth maps $u : B^{3} \to S^{2}$ can be lifted to $u^: B^{3} \to S^{3}$ using the Hopf fibration $h : S^{3} \to S^{2}$ via the factori…

math.AP2025

Rectifiability of entropy productions for weak solutions of the 2D eikonal equation with supercritical regularity

Xavier Lamy, Elio Marconi

Weak solutions $m : Ω \subset R^{2} \to R^{2}$ of the eikonal equation \begin{align*} |m|=1\text{ a.e. and }\mathrm{div}\: m =0\,, \end{align*} arise naturally as shar…

math.AP2025

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…

math.AP2025

The conformal limit for bimerons in easy-plane chiral magnets

Bin Deng, Radu Ignat, Xavier Lamy

We study minimizers $m : R^{2} \to S^{2}$ of the energy functional \begin{align*} E_σ(\boldsymbol{m}) = \int_{\mathbb R^2} \bigg(\frac 12 |\nabla\boldsym…

math.AP2025

Another regularizing property of the 2D eikonal equation

Xavier Lamy, Andrew Lorent, Guanying Peng

A weak solution of the two-dimensional eikonal equation amounts to a vector field $m : Ω \subset R^{2} \to R^{2}$ such that $∣ m ∣ = 1$ a.e. and $div m = 0$ in $\mat…

math.AP2024

On the existence of degenerate solutions of the two-dimensional $H$ -system

André Guerra, Xavier Lamy, Konstantinos Zemas

We consider entire solutions $ω \in H ˙^{1} (R^{2}; R^{3})$ of the $H$ -system $Δ ω = 2 ω_{x} \land ω_{y},$ which we refer to as bubbles. Surprisingly, and contrary to conjectures r…

math.AP2024

On $C^{1}$ regularity for degenerate elliptic equations in the plane

Thibault Lacombe, Xavier Lamy

We show that Lipschitz solutions $u$ of $div G (\nabla u) = 0$ in $B_{1} \subset R^{2}$ are $C^{1}$ , for strictly monotone vector fields $G \in C^{0} (R^{2}; R^{2})$ …

math.AP2024

On regularity and rigidity of $2 \times 2$ differential inclusions into non-elliptic curves

Xavier Lamy, Andrew Lorent, Guanying Peng

We study differential inclusions $D u \in Π$ in an open set $Ω \subset R^{2}$ , where $Π \subset R^{2 \times 2}$ is a compact connected $C^{2}$ curve without rank-one connecti…

math.DG2024

Optimal quantitative stability of the Möbius group of the sphere in all dimensions

André Guerra, Xavier Lamy, Konstantinos Zemas

In any dimension $n \geq 3$ , we prove an optimal stability estimate for the Möbius group among maps $u : S^{n - 1} \to R^{n}$ , of the form $\inf_{λ>0,ϕ\in \mathrm{Mö…

math.AP2023

A symmetry breaking phenomenon for anisotropic harmonic maps from a 2D annulus into $S^{1}$

Andres Contreras, Xavier Lamy

In a two dimensional annulus $A_{ρ} = {x \in R^{2} : ρ < ∣ x ∣ < 1}$ , $ρ \in (0, 1)$ , we characterize $0$ -homogeneous minimizers, in $H^{1} (A_{ρ}; S^{1})$ with respect to their own boun…

Some lifting and approximation properties for maps in W1,2(B3;S2)

Rectifiability of entropy productions for weak solutions of the 2D eikonal equation with supercritical regularity

Global minimality of the Hopf map in the Faddeev-Skyrme model with large coupling constant

The conformal limit for bimerons in easy-plane chiral magnets

Another regularizing property of the 2D eikonal equation

On the existence of degenerate solutions of the two-dimensional H-system

On C1 regularity for degenerate elliptic equations in the plane

On regularity and rigidity of 2×2 differential inclusions into non-elliptic curves

Optimal quantitative stability of the Möbius group of the sphere in all dimensions

A symmetry breaking phenomenon for anisotropic harmonic maps from a 2D annulus into S1

Some lifting and approximation properties for maps in $W^{1, 2} (B^{3}; S^{2})$

On the existence of degenerate solutions of the two-dimensional $H$ -system

On $C^{1}$ regularity for degenerate elliptic equations in the plane

On regularity and rigidity of $2 \times 2$ differential inclusions into non-elliptic curves

A symmetry breaking phenomenon for anisotropic harmonic maps from a 2D annulus into $S^{1}$