Generic scarring for minimal hypersurfaces along stable hypersurfaces
Generic scarring for minimal hypersurfaces along stable hypersurfaces
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DOI：
10.1007/s00039-021-00571-7
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发表时间：
2020-06
影响因子：
2.2
通讯作者：
Antoine Song;Xin Zhou
中科院分区：
文献类型：
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作者：
Antoine Song;Xin Zhou
设是维数的闭流形。我们证明了对于一般的度量M，任何连通的，封闭的，嵌入的，双边的，稳定的，最小的超曲面对应于一个序列的封闭的，嵌入的，最小的超曲面携带沿S，在这个意义上，面积和莫尔斯指数都发散到无穷大，当适当的重整化，收敛到Sas变倍。我们还表明，在大多数封闭的Riemannian 3-manifods中，沿着稳定表面沿着浸入的最小表面会出现疤痕。
Letbe a closed manifold of dimension. We show that for a-generic metricgonM, to any connected, closed, embedded, 2-sided, stable, minimal hypersurfacecorresponds a sequence of closed, embedded, minimal hypersurfacesscarring alongS, in the sense that the area and Morse index ofboth diverge to infinity and, when properly renormalized,converges toSas varifolds. We also show that scarring of immersed minimal surfaces along stable surfaces occurs in most closed Riemannian 3-manifods.