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The extension problem of the mean curvature flow (I)

  • Haozhao LiEmail author
  • Bing Wang
Article

Abstract

We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in \({{\mathbb {R}}}^3\).

Notes

Acknowledgements

H. Z. Li would like to thank Professors T. H. Colding, W. P. Minicozzi II and X. Zhou for insightful discussions. Part of this work was done while he was visiting MIT and he wishes to thank MIT for their generous hospitality. B. Wang would like to thank Professors T. Ilmanen, L. Wang and O. Hershkovits for helpful discussions. Both authors are grateful to the anonymous referees for many useful suggestions to improve the exposition of this paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiChina
  2. 2.The Institute of Geometry and Physics, School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiChina

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