Non-existence of eternal solutions to Lagrangian mean curvature flow with non-negative Ricci curvature
- 37 Downloads
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.
KeywordsMean curvature flow Eternal solution
Mathematics Subject Classification 2010Primary: 53C44 Secondary: 35C06
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.
- 5.Haslhofer, R.: Lectures on curve shortening flow (preprint). http://www.math.toronto.edu/roberth/pde2/curve_shortening_flow.pdf
- 11.Smoczyk, K.: A canonical way to deform a Lagrangian submanifold. arXiv:dg-ga/9605005v2 (1996)