Translating solutions to Lagrangian mean curvature flow
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- by André Neves and Gang Tian PDF
- Trans. Amer. Math. Soc. 365 (2013), 5655-5680 Request permission
Abstract:
We prove some non-existence theorems for translating solutions to Lagrangian mean curvature flow. More precisely, we show that translating solutions with an $L^2$ bound on the mean curvature are planes and that almost-calibrated translating solutions which are static are also planes. Recent work of D. Joyce, Y.-I. Lee, and M.-P. Tsui shows that these conditions are optimal.References
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Additional Information
- André Neves
- Affiliation: Department of Pure Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom
- MR Author ID: 733597
- Email: aneves@imperial.ac.uk
- Gang Tian
- Affiliation: Department of Mathematics, Fine Hall, Princeton University, Princeton, New Jersey 08544
- MR Author ID: 220655
- Email: tian@math.princeton.edu
- Received by editor(s): June 9, 2011
- Published electronically: June 26, 2013
- Additional Notes: The author was partially supported by NSF grant DMS-06-04164.
- © Copyright 2013 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 365 (2013), 5655-5680
- MSC (2010): Primary 53C44, 53D12
- DOI: https://doi.org/10.1090/S0002-9947-2013-05649-8
- MathSciNet review: 3091260