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math.AP2026
Stable solutions in the abelian Higgs model
Marco Badran
We classify entire stable solutions with quadratic energy growth in the -dimensional abelian Higgs model. More precisely, we prove that such solutions are holomorphic with respe…
math.AP2026
A two-dimensional Allen-Cahn theory for interfaces with boundary
Marco Badran, Manuel del Pino, Marco A. M. Guaraco
We develop a two-dimensional Allen-Cahn theory for interfaces with boundary in the line-bundle framework introduced by Fröhlich and Struwe. The central new object is a model soluti…
math.AP2026
Uniform small energy regularity for fractional geometric problems
Marco Badran, Giacomo Cozzi
We prove small energy regularity for a parabolic boundary reaction Ginzburg-Landau problem in the full range , answering a question posed by Hyder, Segatti, Sire and Wa…