The stability of the mean curvature flow in manifolds of special holonomy
The stability of the mean curvature flow in manifolds of special holonomy
复制标题
特殊完整流形中平均曲率流的稳定性
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Mu
中科院分区：
文献类型：
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作者：
Chung;Mu
研究了几种著名的特殊完整流形模型空间中极小子流形的唯一性和平均曲率流的稳定性。这些包括Stenzel度量的余切丛的领域，Calabi度量的余切丛的复杂的射影空间，和布莱恩特-Salamon度量的向量丛在某些爱因斯坦流形。特别是，我们证明了零节，作为校准子流形相对于其各自的环境度量，是唯一的紧凑的极小子流形，是动态稳定的平均曲率流。证明依赖于复杂的互连的Ricci平坦的环境空间和外部几何的校准子流形。
We study the uniqueness of minimal submanifolds and the stability of the mean curvature flow in several well-known model spaces of manifolds of special holonomy. These include the Stenzel metric on the cotangent bundle of spheres, the Calabi metric on the cotangent bundle of complex projective spaces, and the Bryant--Salamon metrics on vector bundles over certain Einstein manifolds. In particular, we show that the zero sections, as calibrated submanifolds with respect to their respective ambient metrics, are unique among compact minimal submanifolds and are dynamically stable under the mean curvature flow. The proof relies on intricate interconnections of the Ricci flatness of the ambient space and the extrinsic geometry of the calibrated submanifolds.