• Corpus ID: 119685060

Nonconvex Surfaces which Flow to Round Points

@article{Mramor2019NonconvexSW,
  title={Nonconvex Surfaces which Flow to Round Points},
  author={Alexander Mramor and Alec Payne},
  journal={arXiv: Differential Geometry},
  year={2019}
}
In this article we extend Huisken's theorem that convex surfaces flow to round points by mean curvature flow. We will construct certain classes of mean convex and non-mean convex hypersurfaces that shrink to round points and use these constructions to create pathological examples of flows. We find a sequence of flows that exist on a uniform time interval, have uniformly bounded diameter, and shrink to round points, yet the sequence of initial surfaces has no subsequence converging in the Gromov… 

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