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Let $\Sigma$ be a compact oriented surface and $N$ a compact K\"ahlermanifold with nonnegative holomorphic bisectional curvature. For a solution ofharmonic map flow starting from an almost-holomorphic map $\Sigma \to N$ (inthe energy sense), the limit at each singular time extends continuously overthe bubble points and no necks appear.

Harmonic map flow for almost-holomorphic maps