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Subsequent singularities of mean convex mean curvature flows in smooth manifolds

Qi Ding Fudan University

Differential Geometry mathscidoc:1912.10003

Calc. Var. Partial Differential Equations, 55, (1), 1-12, 2016
For any n-dimensional smooth manifold $\Sigma$, we show that all the singularities of the mean curvature flow with any initial mean convex hypersurface in $\Sigma$ are cylindrical (of convex type) if the flow converges to a smooth hypersurface $M_\infty$ (maybe empty) at infi nity. Previously this was shown (i) for n$\leq$7, and (ii) for arbitrary n up to the first singular time without the smooth condition on $M_\infty$.
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@inproceedings{qi2016subsequent,
  title={Subsequent singularities of mean convex mean curvature flows in smooth manifolds},
  author={Qi Ding},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224115048886261023},
  booktitle={Calc. Var. Partial Differential Equations},
  volume={55},
  number={1},
  pages={1-12},
  year={2016},
}
Qi Ding. Subsequent singularities of mean convex mean curvature flows in smooth manifolds. 2016. Vol. 55. In Calc. Var. Partial Differential Equations. pp.1-12. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224115048886261023.
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