## Abstract

We consider a compact star-shaped mean convex hypersurface. We prove that in some cases the flow exists until it shrinks to a point. We also prove that in the case of a surface of revolution which is star-shaped and mean convex, a smooth solution always exists up to some finite time T < ∞ at which the flow shrinks to a point asymptotically spherically.

Original language | English (US) |
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Pages (from-to) | 187-215 |

Number of pages | 29 |

Journal | Calculus of Variations and Partial Differential Equations |

Volume | 37 |

Issue number | 1 |

DOIs | |

State | Published - Nov 2009 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

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