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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Translating solutions to Lagrangian mean curvature flow


Authors: André Neves and Gang Tian
Journal: Trans. Amer. Math. Soc. 365 (2013), 5655-5680
MSC (2010): Primary 53C44, 53D12
Published electronically: June 26, 2013
MathSciNet review: 3091260
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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.


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Additional Information

André Neves
Affiliation: Department of Pure Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom
Email: aneves@imperial.ac.uk

Gang Tian
Affiliation: Department of Mathematics, Fine Hall, Princeton University, Princeton, New Jersey 08544
Email: tian@math.princeton.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05649-8
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.
Article copyright: © Copyright 2013 American Mathematical Society