On the blow-up of harmonic maps from surfaces to homogeneous manifolds

Abstract

We study harmonic map sequences from surfaces to compact homogeneous spaces. For sequences developing a single bubble, we derive refined asymptotic expansions in the neck region and prove new obstruction relations among the leading coefficients. These strengthen earlier results by converting an inequality into an equality. For weakly conformal maps, this yields geometric constraints: in low dimensions the tangent planes of the limit map and bubble must coincide, while in higher dimensions they are isoclinic.