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math.AP2026
Parabolic defect measures for Harmonic Maps with Free Boundary
Anirban Das, Ali Hyder, Yannick Sire
We introduce defect measures for the heat flow of a class of harmonic maps with free boundary and initiate their analysis. Our flow is motivated by singular perturbations on the bo…
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 , if two disjoint interval…