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Construction of High Codimension Ancient Mean Curvature Flows

Differential Geometry 2019-09-06 v2

Abstract

We construct a class of compact ancient solutions to the mean curvature flow in Euclidean space with high codimension. In particular, we construct higher codimensional ancient curve shortening flows. Moreover, we characterize the asymptotic behavior of these solutions. Add on remark: the construction in this paper has been discovered by Altschuler D.-Altschuler S.-Angenent-Wu in [AAAW13].

Keywords

Cite

@article{arxiv.1908.02688,
  title  = {Construction of High Codimension Ancient Mean Curvature Flows},
  author = {Douglas Stryker and Ao Sun},
  journal= {arXiv preprint arXiv:1908.02688},
  year   = {2019}
}

Comments

10 pages, comments are welcomed! After the first version of this preprint was uploaded to arxiv, we discovered that the construction in this paper has been discovered by Altschuler D.-Altschuler S.-Angenent-Wu in [AAAW13]. Since the motivation of our preprint is different from [AAAW13], we still hope the readers could find some innovating ideas from this preprint

R2 v1 2026-06-23T10:42:12.475Z