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$\mathcal{H}-$holomorphic curves are solutions of a specific modification ofthe pseudoholomorphic curve equation in symplectizations involving a harmonic$1-$form as perturbation term. In this paper we compactify the moduli space of$\mathcal{H}-$holomorphic curves with a priori bounds on the harmonic$1-$forms.

A Compactness Result for $\mathcal{H}-$holomorphic Curves in Symplectizations