Abstract

We show that any harmonic sequence determined by a harmonic map from a compact Riemannian surface M to ℂℙn has a terminating holomorphic (or anti-holomorphic) map from M to ℂℙn, or a “bubble tree limit” consisting of a harmonic map \( \hat f \): M → ℂℙn and a tree of bubbles hλµ: S2 → ℂℙn.

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