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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Closed Riemannian manifolds with compact isometric group actions contain infinitely many invariant minimal hypersurfaces, and under a finiteness assumption each G-homology class contains infinitely many distinct embedded realizations.
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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.
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Infinite existence of equivariant minimal hypersurfaces
Closed Riemannian manifolds with compact isometric group actions contain infinitely many invariant minimal hypersurfaces, and under a finiteness assumption each G-homology class contains infinitely many distinct embedded realizations.