Every Riemannian manifold diffeomorphic to S^{3} contains at least two distinct embedded minimal 2-spheres.
Chun-Pong Chu,Minimal surfaces with arbitrary genus in3-spheres of positive Ricci curvature
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
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.
fields
math.DG 2years
2026 2representative citing papers
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 three non-planar minimal spheres in suitable ellipsoids.
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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 three non-planar minimal spheres in suitable ellipsoids.