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.
Equivariant min-max theory
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We develop an equivariant min-max theory as proposed by Pitts-Rubinstein in 1988 and then show that it can produce many of the known minimal surfaces in $\mathbb{S}^3$ up to genus and symmetry group. We also produce several new infinite families of minimal surfaces in $\mathbb{S}^3$ proposed by Pitts-Rubinstein. These examples are doublings and desingularizations of stationary integral varifolds in $\mathbb{S}^3$.
fields
math.DG 2years
2026 2representative citing papers
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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.
- Embedded minimal $S^1$-bundles in $\mathbb{S}^4$