Abstract
The compactness theorem of the closed embedded minimal surfaces of fixed genus in a 3-dimensional closed Riemannian manifoldN is proved, providedN is simply connected and the nonpositive value set of Ricci curvature is sufficiently concentrated within finite balls and the minimal surfaces are uniformly away from these balls.
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Lee, Y., Wu, D. The closed embedded minimal surfaces in an almost positively curved three manifold. Ann Glob Anal Geom 13, 231–237 (1995). https://doi.org/10.1007/BF00773657
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DOI: https://doi.org/10.1007/BF00773657