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Curvature flow with driving force on fixed boundary points

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Abstract

In this paper, we consider the curvature flow with driving force on fixed boundary points in the plane. We give a general local existence and uniqueness result of this problem with \(C^2\) initial curve. For a special family of initial curves, we classify the solutions into three categories. Moreover, in each category, the asymptotic behavior is given.

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Acknowledgements

The author is grateful to Professor Matano Hiroshi for his inspiring suggestion about Grim reaper argument. He is also grateful to Professor Giga Yoshikazu for letting me know several related useful papers. The author is grateful to the anonymous referee for valuable suggestions to improve the presentation of this paper. The author is the Research Fellow of Japan Society for the Promotion of Science, Number: 17J05160. This research is supported by Japan Society for the Promotion of Science

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  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo, 153-8914, Japan

    Longjie Zhang

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  1. Longjie Zhang
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Correspondence to Longjie Zhang.

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We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

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Zhang, L. Curvature flow with driving force on fixed boundary points. J Geom Anal 28, 3491–3521 (2018). https://doi.org/10.1007/s12220-017-9967-0

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