Gromov convergence of pseudoholomorphic disks

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Rigidity and uniruling for Lagrangian submanifolds (2008, methodology): “For this, besides the transversality results described before, we only need the Gromov compactness theorem (for disks see Frauenfelder [31]).”
On the homological mirror symmetry conjecture for pairs of pants (2010, methodology): “The space of possible stable pearls corresponding to vertices of TS is compact, by standard Gromov compactness as in [18].”
Floer cohomology and pencils of quadrics (2010, background): “The general description of a Gromov-Floer limit of disks as a tree of holomorphic disks and sphere bubbles, see for instance [35], implies that u∞ has at least one disk component inside C1, with boundary on KL, and that any component of u∞ meeting C0\(C0 ∩ C1) must be a rational curve, since L ∩ C0 ”
Homological mirror symmetry for Calabi–Yau hypersurfaces in projective space (2011, unknown): “We observe that each moduli space has bounded energy, and standard Gromov compactness shows that any sequence in one of these moduli spaces has a subsequence which converges, up to sphere and disk bubbling (see [34] for spheres and [14] for disks).”