L. Martinazzi

collaborators

3 papers

math.AP2026

Non-constancy and multiplicity of half-harmonic maps from intervals into the circle

Ali Hyder, Luca Martinazzi

We study one-dimensional half-harmonic maps from the real line into the circle with prescribed exterior data. We show that, for every positive integer $k$ , if two disjoint interval…

math.DG2025

Gluing instantons Ã la Brezis-Coron in dimension four and the dipole construction

Luca Martinazzi, Tristan RiviÃ¨re

Given a connection $A$ on a $S U (2)$ -bundle $P$ over $R^{4}$ with finite Yang-Mills energy $Y M (A)$ and nonzero curvature $F_{A} (0)$ at the origin, and given $I ¨ > 0$ small enough…

math.AP2025

One-dimensional half-harmonic maps into the circle and their degree

Luca Martinazzi, Ali Hyder

Given a half-harmonic map $u \in H ˙^{\frac{1}{2}, 2} (R, S^{1})$ minimizing the fractional Dirichlet energy under Dirichlet boundary conditions in $\mathbb{R}\setmi…