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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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.