Decay of excess for the abelian Higgs model

Guido De Philippis, Aria Halavati, Alessandro Pigati

In this article we prove that entire critical points $(u,\nabla )$ of the self-dual $U(1)$-Yang-Mills-Higgs functional $E_1$, with energy $$E_1(u,\nabla;B_R):=\int_{B_R}\left[|\nabl…