The stability of the mean curvature flow in manifolds of special holonomy

Chung-Jun Tsai National Taiwan University Mu-Tao Wang Columbia University

Differential Geometry Geometric Analysis and Geometric Topology mathscidoc:1608.10026

2016.5
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.
mean curvature flow, Stenzel metric, cotangent bundle, cotangent bundle, Bryant--Salamon metrics
[ Download ] [ 2016-08-20 16:20:36 uploaded by mutaowang ] [ 149 downloads ] [ 0 comments ]
@inproceedings{chung-jun2016the,
  title={The stability of the mean curvature flow in manifolds of special holonomy},
  author={Chung-Jun Tsai, and Mu-Tao Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160820162036210142330},
  year={2016},
}
Chung-Jun Tsai, and Mu-Tao Wang. The stability of the mean curvature flow in manifolds of special holonomy. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160820162036210142330.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved