The Existence of Harmonic Maps from an Annulus to S² with Symmetric Boundary Value

In this paper, we use the deformation method and G-equivariant theory to prove the existence and multiplicity of harmonic maps from an annulus to the unit sphere in R³ with symmetric boundary value. In particular, we can get infinitely many homotopically different harmonic maps if the boundary value is S¹-equivariant and nonconstant.