6 papers
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…
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…
Carleman estimates for stationary -valued maps: a variational approach
Aria Halavati, Luca Spolaor
We prove a Carleman-type estimate for Dirichlet-stationary multivalued functions and apply it to give a different proof of the optimal dimension of the singular set of Dir-minimizi…
Decay of excess for the abelian Higgs model
Guido De Philippis, Aria Halavati, Alessandro Pigati
In this article we prove that entire critical points of the self-dual -Yang-Mills-Higgs functional , with energy $$E_1(u,\nabla;B_R):=\int_{B_R}\left[|\nabl…
New weighted inequalities on two-manifolds
Aria Halavati
We establish a new class of weighted Poincaré and elliptic functional inequalities on smooth two-manifolds with explicit constants, for a family of weights satisfying a diffe…
Quantitative stability of Yang-Mills-Higgs instantons in two dimensions
Aria Halavati
We prove that if an N-vortex pair nearly minimizes the Yang-Mills-Higgs energy, then it is second order close to a minimizer. First we use new weighted inequalities in two dimensio…