This research uncovers embedded minimal surfaces in 3-spheres, suggesting robust topological properties.
We describe some topological structure in the set of all surfaces with finitely many singularities in the 3-sphere. As an application, we prove that every Riemannian 3-sphere of positive Ricci curvature contains, for every g, a genus g embedded minimal surface with area at most twice the first Simon-Smith width of the ambient 3-sphere.
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Adrian Chun-Pong Chu (2025) studied this question.
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