Isolated singularities conjecture for properly embedded minimal surfaces

Let BB be a closed geodesic ball in a Riemannian three-manifold, and let MM be a minimal surface with boundary MB\partial M \subset \partial B. Suppose that MM is properly embedded in BB punctured at the center of the ball. Isolated singularities conjecture. The surface MM extends across the puncture to a smooth compact embedded minimal surface in BB. This is a removable-singularity assertion for properly embedded minimal surfaces; the supplied source does not state whether it has been resolved.

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Primary source

William H. Meeks and Michael Wolf, “Minimal surfaces with the area growth of two planes; the case of infinite symmetry”, arXiv:math/0501110 (2005).

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