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math.DG2026
Integral curvature estimates and geodesic limits for stable abelian Higgs fields
Marco Badran, Marco A. M. Guaraco, Aria Halavati
We prove that, on closed three-manifolds, the limit interface of a sequence of stable abelian Higgs critical points with uniformly bounded energy is a finite union of smooth closed…
math.DG2026
Min-Max Construction of Anisotropic Minimal Surfaces with Genus Bound
Antonio De Rosa, Aria Halavati, Ling Wang
We establish an anisotropic analogue of the celebrated theorem of Meeks-Simon-Yau: every minimizing sequence of surfaces within a fixed isotopy class converges to a smooth stable a…