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

令\(M^{n+1}\)是维度为\(3\le n+1\le 7\)的封闭流形。我们表明，对于M上的\(C^\infty \) -泛型度量g，对于任何连接的、封闭的、嵌入的、2 边的、稳定的、最小的超曲面\(S\subset (M,g)\)对应于沿着S的封闭的、嵌入的、最小的超曲面序列\(\{\Sigma _k\}\)疤痕，从某种意义上说\(\Sigma _k\)的面积和莫尔斯指数都发散到无穷大，并且当适当地重新归一化时，\(\Sigma _k\)收敛到S作为杂色。我们还表明，在大多数封闭的黎曼 3 流形中，沿稳定表面浸入的最小表面的疤痕发生。