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1 April 2016 Uniqueness results for special Lagrangians and Lagrangian mean curvature flow expanders in Cm
Yohsuke Imagi, Dominic Joyce, Joana Oliveira dos Santos
Duke Math. J. 165(5): 847-933 (1 April 2016). DOI: 10.1215/00127094-3167275

Abstract

We prove two main results. (1) Suppose that L is a closed, embedded, exact special Lagrangian m-fold in Cm asymptotic at infinity to the union Π1Π2 of two transverse special Lagrangian planes Π1,Π2 in Cm for m3. Then L is one of the explicit Lawlor neck family of examples found by Lawlor. (2) Suppose that L is a closed, embedded, exact Lagrangian mean curvature flow expander in Cm asymptotic at infinity to the union Π1Π2 of two transverse Lagrangian planes Π1,Π2 in Cm for m3. Then L is one of the explicit family of examples in recent work by Joyce, Lee, and Tsui. If instead L is immersed rather than embedded, the only extra possibility in (1), (2) is L=Π1Π2. Our methods, which are new and can probably be used to prove other similar uniqueness theorems, involve J-holomorphic curves, Lagrangian Floer cohomology, and Fukaya categories from symplectic topology.

Citation

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Yohsuke Imagi. Dominic Joyce. Joana Oliveira dos Santos. "Uniqueness results for special Lagrangians and Lagrangian mean curvature flow expanders in Cm." Duke Math. J. 165 (5) 847 - 933, 1 April 2016. https://doi.org/10.1215/00127094-3167275

Information

Received: 3 April 2014; Revised: 30 April 2015; Published: 1 April 2016
First available in Project Euclid: 10 December 2015

zbMATH: 1341.53115
MathSciNet: MR3482334
Digital Object Identifier: 10.1215/00127094-3167275

Subjects:
Primary: 53D12
Secondary: 53A10, 53C44, 53D40

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 5 • 1 April 2016
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