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Non-existence of eternal solutions to Lagrangian mean curvature flow with non-negative Ricci curvature

  • Keita Kunikawa
Original Paper
  • 37 Downloads

Abstract

In this paper, we derive a mean curvature estimate for eternal solutions of uniformly almost calibrated Lagrangian mean curvature flow with non-negative Ricci curvature in the complex Euclidean space. As a consequence, we show a non-existence result for such eternal solutions.

Keywords

Mean curvature flow Eternal solution 

Mathematics Subject Classification 2010

Primary: 53C44 Secondary: 35C06 

Notes

Acknowledgements

The author is supported by Grant-in-Aid for JSPS Fellows Number 16J01498. During the preparation of this paper the author has stayed at the Max Planck Institute for Mathematics in the Sciences, Leipzig. The author is grateful to Jürgen Jost for his hospitality and his interest. Reiko Miyaoka also gave the author helpful comments in private seminars. Finally, the author would like to thank the referees for their valuable comments which helped to improve the manuscript.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Advanced Institute for Materials ResearchTohoku UniversitySendaiJapan

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