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Reference: Imagi, Yohsuke, Joyce, Dominic and Santos, Joana, (2015). Uniqueness results for special Lagrangians and Lagrangian mean curvature flow expanders in C^m. Duke Mathematical Journal, 165 (5), 847-933.Citable link to this page:

 

Uniqueness results for special Lagrangians and Lagrangian mean curvature flow expanders in C^m

Abstract: We prove two main results: (a) Suppose $L$ is a closed, embedded, exact special Lagrangian $m$-fold in${\mathbb C}^m$ for $m\ge 3$ asymptotic at infinity to the union$\Pi_1\cup\Pi_2$ of two transverse special Lagrangian planes $\Pi_1,\Pi_2$ in${\mathbb C}^m$. Then $L$ is one of the explicit 'Lawlor neck' family ofexamples found by Lawlor (Invent. math. 95, 1989). (b) Suppose $L$ is a closed, embedded, exact Lagrangian mean curvature flowexpander in ${\mathbb C}^m$ for $m\ge 3$ asymptotic at infinity to the union$\Pi_1\cup\Pi_2$ of two transverse Lagrangian planes $\Pi_1,\Pi_2$ in ${\mathbbC}^m$. Then $L$ is one of the explicit family of examples found by Joyce, Leeand Tsui, arXiv:0801.3721. If instead $L$ is immersed rather than embedded, the only extra possibilityin (a),(b) is $L=\Pi_1\cup\Pi_2$. Our methods, which are new and can probably be used to prove other similaruniqueness theorems, involve $J$-holomorphic curves, Lagrangian Floercohomology, and Fukaya categories from symplectic topology. When $m=2$, (a) iseasy to prove using hyperkahler geometry, and (b) is proved by Lotay and Neves,arXiv:1208.2729.

Peer Review status:Peer reviewedPublication status:PublishedVersion:Accepted ManuscriptNotes:Copyright © 2014 Duke Mathematical Journal. This article has been accepted for publication in Duke Mathematical Journal, Published by Duke University Press.

Bibliographic Details

Publisher: Duke University Press

Publisher Website: http://www.dukeupress.edu/

Journal: Duke Mathematical Journalsee more from them

Publication Website: http://www.dukeupress.edu/Duke-Mathematical-Journal/

Issue Date: 2015

pages:847-933Identifiers

Urn: uuid:7d9026c3-35cb-4a8d-9ffe-af179cc85bf6

Source identifier: 459672

Eissn: 1547-7398

Doi: https://doi.org/10.1215/00127094-3167275

Issn: 0012-7094 Item Description

Type: Journal article;

Version: Accepted ManuscriptKeywords: special Lagrangian Lagrangian mean curvature flow Lagrangian MCF expander Calabi-Yau manifold Lagrangian Floer cohomology Fukaya category J-holomorphic curves Tiny URL: pubs:459672

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Autor: Imagi, Yohsuke - - - Joyce, Dominic - institutionUniversity of Oxford Oxford, MPLS, Mathematical Inst - - - Santos, Joana - - - -

Fuente: https://ora.ox.ac.uk/objects/uuid:7d9026c3-35cb-4a8d-9ffe-af179cc85bf6



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