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

TL;DR

This paper investigates the behavior of harmonic maps from surfaces to homogeneous spaces, deriving refined asymptotics and geometric constraints for bubble formation and tangent plane relations.

Contribution

It provides new asymptotic expansions and obstruction relations for harmonic map sequences, strengthening previous inequalities to equalities and revealing geometric constraints.

Findings

Refined asymptotic expansions in the neck region for bubble sequences

Obstruction relations among leading coefficients of bubbles

Geometric constraints on tangent planes in low and high dimensions

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.