The Existence of Embedded G-Invariant Minimal Hypersurface
Abstract
For a compact connected Lie group G acting as isometries on a compact orientable Riemannian manifold Mn+1, and cohomogeneity not equal to 0 or 2, we prove the existence of a nontrivial embedded G-invariant minimal hypersurface, that is smooth outside a set of Hausdorff dimension at most $n-7.
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