Generic density of equivariant min-max hypersurfaces

Tongrui Wang

doi:10.1016/j.jfa.2025.110979

paper

Generic density of equivariant min-max hypersurfaces

arXiv:2309.09527 · doi:10.1016/j.jfa.2025.110979

Abstract

For a compact Riemannian manifold $M^{n + 1}$ acted isometrically on by a compact Lie group $G$ with cohomogeneity $Cohom (G) \geq 2$ , we show the Weyl asymptotic law for the $G$ -equivariant volume spectrum. As an application, we show in the $C_{G}^{\infty}$ -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 $\partial M$ .

31 pages, 2 figures. Final accepted version, published in JFA

References in corpus (1)

Min-max theory for $G$ -invariant minimal hypersurfaces