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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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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DOI: https://doi.org/10.1007/s12220-017-9967-0