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SO(n)-Invariant special Lagrangian submanifolds of ℂ n+1 with fixed loci

dc.contributor.author Bryant, RL
dc.date.accessioned 2016-08-25T13:51:41Z
dc.date.issued 2006-01-01
dc.identifier.issn 0252-9599
dc.identifier.uri https://hdl.handle.net/10161/12682
dc.description.abstract Let SO(n) act in the standard way on ℂn and extend this action in the usual way to ℂn+1 = ℂ ⊕ ℂ n . It is shown that a nonsingular special Lagrangian submanifold L ⊂ ℂn+1 that is invariant under this SO(n)-action intersects the fixed ℂ ⊂ ℂ n+1 in a nonsingular real-analytic arc A (which may be empty). If n > 2, then A has no compact component. Conversely, an embedded, noncompact nonsingular real-analytic arc A ⊂ ℂ lies in an embedded nonsingular special Lagrangian submanifold that is SO(n)-invariant. The same existence result holds for compact A if n = 2. If A is connected, there exist n distinct nonsingular SO(n)-invariant special Lagrangian extensions of A such that any embedded nonsingular SO(n)-invariant special Lagrangian extension of A agrees with one of these n extensions in some open neighborhood of A. The method employed is an analysis of a singular nonlinear PDE and ultimately calls on the work of Gérard and Tahara to prove the existence of the extension. © The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2006.
dc.publisher Springer Science and Business Media LLC
dc.relation.ispartof Chinese Annals of Mathematics. Series B
dc.relation.isversionof 10.1007/s11401-005-0368-5
dc.title SO(n)-Invariant special Lagrangian submanifolds of ℂ n+1 with fixed loci
dc.type Journal article
duke.contributor.id Bryant, RL|0110365
pubs.begin-page 95
pubs.end-page 112
pubs.issue 1
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.organisational-group Trinity College of Arts & Sciences
pubs.publication-status Published
pubs.volume 27
dc.identifier.eissn 1860-6261
duke.contributor.orcid Bryant, RL|0000-0002-4890-2471


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