Every Riemannian manifold diffeomorphic to S^{3} contains at least two distinct embedded minimal 2-spheres.
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math.DG 4years
2026 4representative citing papers
A capillary interpolation framework produces new minimal surfaces in spheres as non-trivial sphere bundles over base spaces including Stiefel manifolds, projective planes over division algebras, and Lie group quotients, with uniqueness for rotationally symmetric cases.
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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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.