Generic scarring for minimal hypersurfaces along stable hypersurfaces

Let $$M^{n+1}$$ be a closed manifold of dimension $$3\le n+1\le 7$$ . We show that for $$C^\infty $$ -generic metric g on M, to any connected, closed, embedded, 2-sided, stable, minimal hypersurface $$S\subset (M,g)$$ corresponds sequence hypersurfaces $$\{\Sigma _k\}$$ scarring along S, in the sense area and Morse index $$\Sigma _k$$ both diverge infinity and, when properly renormalized, converges S as varifolds. also immersed surfaces stable occurs most Riemannian 3-manifods.