Properly embedded minimal surfaces with finite total curvature

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The Geometry of Minimal Surfaces of Finite Genus I: Curvature Estimates and Quasiperiodicity (2004, unknown): “This fact, together with a standard diagonal argument has as a consequence the following lemma; see Theorem 4.39 in [ 29 ] or the proof of Theorem 1.6 in [26] for a similar analysis.”
The theory of minimal surfaces in M × R (2005, unknown): “Every sequence of properly embedded minimal surfaces in a Riemannian threemanifold, which satisfy uniform local area and local curvature estimates and such that each surface in the sequence intersects some compact domain, has a subsequence that converges to a properly embedded minimal surface with t”
Conformal properties in classical minimal surface theory (2004, methodology): “A standard compactness result (see for example [80] or [107]) shows that a subsequence of the D̃n converges uniformly on compact sets of R(3) to an orientable, complete, simply-connected, immersed minimal surface D̃∞ passing through the origin, with bounded Gaussian curvature KD̃∞ , KD̃∞(0) = −1 and”