André Guerra

activity

20232026

collaborators

7 papers

math.AP2026

Minimizing tangent maps into complex projective space

Matilde Gianocca, André Guerra, David Ziener

We classify all nonconstant smooth harmonic maps $S^{2} \to CP^{n}$ and $S^{3} \to CP^{n}$ whose 0-homogeneous extensions are minimizing: they are, respec…

math.AP2026

A singular minimizer of a smooth strongly polyconvex functional in two dimensions

André Guerra, Riccardo Tione

We construct a Lipschitz, non- $C^{1}$ map $u : R^{2} \to R^{6}$ which is the unique global minimizer of a smooth, strongly polyconvex functional. Such an example is…

math.AP2026

Stationary points of conformally invariant polyconvex energies

André Guerra, Riccardo Tione

We consider polyconvex integrands that are conformally invariant and frame indifferent. In two dimensions, we prove that the corresponding stationary points are smooth outside a di…

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

Constancy of the index for gradient mappings

André Guerra, Riccardo Tione

We show that if the Hessian of a $C^{1, 1}$ function has uniformly positive determinant almost everywhere then its index is locally constant, as conjectured by Šverák in 1992. We de…

math.AP2024

Regularity and compactness for critical points of degenerate polyconvex energies

André Guerra, Riccardo Tione

We study Lipschitz critical points of the energy $\int_{Ω} g (det D u) d x$ in two dimensions, where $g$ is a strictly convex function. We prove that the Jacobian of any Lipschitz…

math.AP2023

Unique continuation for differential inclusions

Guido De Philippis, André Guerra, Riccardo Tione

We consider the following question arising in the theory of differential inclusions: given an elliptic set $Γ$ and a Sobolev map $u$ whose gradient lies in the quasiconformal envel…

Minimizing tangent maps into complex projective space

A singular minimizer of a smooth strongly polyconvex functional in two dimensions

Stationary points of conformally invariant polyconvex energies

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

Constancy of the index for gradient mappings

Regularity and compactness for critical points of degenerate polyconvex energies

Unique continuation for differential inclusions

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