• 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}
}```
• Published 9 January 2019
• Mathematics
• arXiv: Differential Geometry
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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