### 摘要

We consider the expansion of a convex closed plane curve C_{0} along its outward normal direction with speed G(1/k), where k is the curvature and (Formula presented.) is a strictly increasing function. We show that if (Formula presented.), then the isoperimetric deficit (Formula presented.) of the flow converges to zero. On the other hand, if (Formula presented.), then for any number d ≥ 0 and (Formula presented.), one can choose an initial curve C_{0} so that its isoperimetric deficit D(t) satisfies (Formula presented.) for all t ∈[0, ∞). Hence, without rescaling, the expanding curve C_{t} will not become circular. It is close to some expanding curve P_{t}, where each P_{t} is parallel to P_{0}. The asymptotic speed of P_{t} is given by the constant λ.

原文 | English |
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頁（從 - 到） | 779-794 |

頁數 | 16 |

期刊 | Journal of Evolution Equations |

卷 | 14 |

發行號 | 4-5 |

DOIs | |

出版狀態 | Published - 2014 一月 1 |

### 指紋

### All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)

### 引用此

*Journal of Evolution Equations*,

*14*(4-5), 779-794. https://doi.org/10.1007/s00028-014-0238-2