Matilde Gianocca

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math.DG2025

Note on energy index and first eigenvalue of minimal surfaces in spheres

Matilde Gianocca

A minimal immersion from a surface to $S^{3}$ can be viewed both as a critical point of the area and of the energy. Although no difference appears at first order, looking at the resp…

math.DG2025

Rigidity in the Ginzburg--Landau approximation of harmonic spheres

Matilde Gianocca

We prove that not every harmonic map from $S^{2}$ to $S^{2}$ can arise as a limit of Ginzburg--Landau critical points. More precisely, we show that the only degree-one harmonic map…

math.DG2024

Morse Index Stability for the Ginzburg-Landau Approximation

Francesca Da Lio, Matilde Gianocca

In this paper we study the behaviour of critical points of the Ginzburg-Landau perturbation of the Dirichlet energy into the sphere $E_\varepsilon(u):=\int_Σ\frac{1}{2}|du|^2_h\ \,…