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Proceedings of the American Mathematical Society Series B

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Global existence for the minimal surface equation on $\mathbb {R}^{1,1}$


Author: Willie Wai Yeung Wong
Journal: Proc. Amer. Math. Soc. Ser. B 4 (2017), 47-52
MSC (2010): Primary 35B35, 58J45
DOI: https://doi.org/10.1090/bproc/25
Published electronically: November 29, 2017
MathSciNet review: 3730736
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Abstract: In a 2004 paper, Lindblad demonstrated that the minimal surface equation on $\mathbb {R}^{1,1}$ describing graphical timelike minimal surfaces embedded in $\mathbb {R}^{1,2}$ enjoy small data global existence for compactly supported initial data, using Christodoulou’s conformal method. Here we give a different, geometric proof of the same fact, which exposes more clearly the inherent null structure of the equations, and which allows us to also close the argument using relatively few derivatives and mild decay assumptions at infinity.


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Additional Information

Willie Wai Yeung Wong
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
MR Author ID: 877992
ORCID: 0000-0002-5050-2119
Email: wongwwy@member.ams.org

Received by editor(s): January 6, 2016
Published electronically: November 29, 2017
Additional Notes: The author thanks the Tsinghua Sanya International Mathematics Forum, Sanya, Hainan, People’s Republic of China; as well as the National Center for Theoretical Sciences, Mathematics Division, National Taiwanese University, Taipei, Taiwan, for their hospitality during the period in which this research was performed.
Communicated by: Joachim Krieger
Article copyright: © Copyright 2017 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)