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Examples of stable embedded minimal spheres without area bounds

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arxiv 0812.3841 v2 pith:X6PE2YDM submitted 2008-12-19 math.DG math.GT

Joel I. Kramer This is my paper · ORCID
classification math.DGmath.GT
keywords areaembeddedminimalspheresthereanalogousauthorbounds
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The author proves that there is an open non empty set of metrics on any 3-manifold such that there exists a family of stably embedded minimal 2-spheres whose area is unbounded. This generalizes the work of T. Colding and W. Minicozzi who have shown an analogous result for the torus and B. Dean who showed the positive genus case.

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  1. Closed minimal surfaces of index one in Riemannian manifolds

    math.DG 2026-06 unverdicted novelty 5.0 of 10

    Existence of index-one minimal hypersurfaces with unbounded volume in enlargeable manifolds (dims 3-7) plus 3D scalar curvature rigidity under area-nonincreasing maps.

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