Generic density of equivariant min-max hypersurfaces

Tongrui Wang

doi:10.1016/j.jfa.2025.110979

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arXiv · 2309.09527

Generic density of equivariant min-max hypersurfaces

Tongrui Wang

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Abstract

For a compact Riemannian manifold $M^{n+1}$ acted isometrically on by a compact Lie group $G$ with cohomogeneity ${\rm Cohom}(G)\geq 2$, we show the Weyl asymptotic law for the $G$-equivariant volume spectrum. As an application, we show in the $C^\infty_G$-generic sense with a certain dimension assumption that the union of min-max minimal $G$-hypersurfaces (with free boundary) is dense in $M$, whose boundaries' union is also dense in $\partial M$.

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Tongrui Wang. 2023-09-18. Generic density of equivariant min-max hypersurfaces. https://doi.org/10.1016/j.jfa.2025.110979

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