A symmetry breaking phenomenon for anisotropic harmonic maps from a 2D annulus into ${\mathbb{S}}^1$

Andres Contreras, Xavier Lamy

In a two dimensional annulus $A_{\rho }=\{x\in {\mathbb{R}}^2:\rho <|x|<1\}$, $\rho \in (0,1)$, we characterize $0$-homogeneous minimizers, in $H^1(A_{\rho };{\mathbb{S}}^1)$ with respect to their own boun…