Examples of stable embedded minimal spheres without area bounds

2008/12/19 by Joel Israel Kramer, Kramer, Joel I.
Mathematics · #49Q05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.0812.3841

openalex publication_date 2008/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

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