Papers and preprints

1. Stable solutions in the abelian Higgs model.
   M. Badran. Submitted. arXiv.
2. A two-dimensional Allen-Cahn theory for interfaces with boundary.
   M. Badran, M. del Pino and M. A. M. Guaraco. Submitted. arXiv.
3. Uniform small energy regularity for fractional geometric problems.
   M. Badran and G. Cozzi. Submitted. arXiv.
4. Nonlocal free boundary minimal surfaces.
   M. Badran, S. Dipierro and E. Valdinoci. To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. arXiv.
5. Stationary $p$-harmonic maps approaching planar singular harmonic maps to the circle.
   M. Badran and J. Van Schaftingen. Calc. Var. PDE. Journal. arXiv.
6. Harmonic maps to the circle with higher dimensional singular set.
   M. Badran. Proc. London Math. Soc. Journal. arXiv.
7. Solutions of the Ginzburg-Landau equations concentrating on codimension-2 minimal submanifolds.
   M. Badran and M. del Pino. J. London Math. Soc. Journal. arXiv.
8. Entire solutions to 4-dimensional Ginzburg-Landau equations and codimension 2 minimal submanifolds.
   M. Badran and M. del Pino. Adv. Math. Journal. arXiv.

AI-discovered proofs

This section collects papers whose proofs were first produced by AI through a series of interactions with the authors. Our role was to check the arguments and rework the proofs, clarifying the underlying ideas and making them accessible to the mathematical community.

1. Integral curvature estimates and geodesic limits for stable abelian Higgs fields.
   M. Badran, M. A. M. Guaraco and A. Halavati. arXiv.