Aria Halavati

Decay of excess for the abelian Higgs model

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})\leq(1+\tau(n))\cdot2\pi\omega_{n-2}R^{n-2} for all R>0 , have unique blow-down. Moreover, we show that they are two-dimensional in ambient...