Generic scarring for minimal hypersurfaces along stable hypersurfaces - Song, Antoine; Zhou, Xin (Geometric and functional analysis, 2021)
Let M n + 1 be a closed manifold of dimension 3 ≤ n + 1 ≤ 7 . We show that for a C ∞ -generic metric g on M , to any connected, closed, embedded, 2-sided, stable, minimal hypersurface S ⊂ ( M , g ) corresponds a sequence of closed, embedded, minimal hypersurfaces { Σ k } scarring along S , in the sense that the area and Morse index of Σ k both diverge to infinity and, when properly renormalized, Σ k converges to S as varifolds. We also show that scarring of immersed minimal surfaces along stable surfaces occurs in most closed Riemannian 3-manifods.