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Minimal surfaces with arbitrary genus in 3-spheres of positive Ricci curvature
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Minimal surfaces with arbitrary genus in 3-spheres of positive Ricci curvature
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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.
Forward citations
Cited by 2 Pith papers
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Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric
Every Riemannian manifold diffeomorphic to S^{3} contains at least two distinct embedded minimal 2-spheres.
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Minimal spheres and scalar curvature
In 3-spheres with positive Ricci curvature and scalar curvature at least Lambda_0 > 0, there exist four distinct embedded minimal 2-spheres with areas at most 12 pi (i+1)/Lambda_0, plus an application showing at least...
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