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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Mean curvature flow of asymptotically conical Lagrangian submanifolds


Author: Wei-Bo Su
Journal: Trans. Amer. Math. Soc. 373 (2020), 1211-1242
MSC (2010): Primary 53C44; Secondary 52C38
DOI: https://doi.org/10.1090/tran/7946
Published electronically: October 28, 2019
MathSciNet review: 4068262
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Abstract: In this paper, we study Lagrangian mean curvature flow (LMCF) of asymptotically conical (AC) Lagrangian submanifolds asymptotic to a union of special Lagrangian cones. Since these submanifolds are non-compact, we establish a short-time existence theorem for AC LMCF first. Then we focus on the equivariant, almost-calibrated case and prove long-time existence and convergence results. In particular, under certain smallness assumptions on the initial data, we show that the equivariant, almost-calibrated AC LMCF converges to a Lagrangian catenoid or an Anciaux’s expander.


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Wei-Bo Su
Affiliation: Department of Mathematics, National Taiwan University, Taipei, Taiwan
Email: d03221004@ntu.edu.tw

Received by editor(s): March 5, 2019
Received by editor(s) in revised form: June 30, 2019
Published electronically: October 28, 2019
Article copyright: © Copyright 2019 American Mathematical Society