A note on n -axially symmetric harmonic maps from B3B3 to S2S2 minimizing the relaxed energy

For any n⩾2n⩾2 we provide an explicit example of an n  -axially symmetric map u∈H1(B2,S2)∩C0(B¯2∖B¯1), where Br={p∈R3:|p|0Σ(u,B2)>0, u|B1≢constu|B1≢const. Here Σ(u,B2)Σ(u,B2) is (in a generalized sense) the lenght of a minimal connection joining the topological singularities of u  . By “strictly minimizing in B1B1” we intend that F(u,B2)