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Stability of torsion-free G_2 structures along the Laplacian flow

Abstract:
We prove that torsion-free G_2 structures are (weakly) dynamically stable along the Laplacian flow for closed G_2 structures. More precisely, given a torsion-free G_2 structure $\varphi$ on a compact 7-manifold, the Laplacian flow with initial value cohomologous and sufficiently close to $\varphi$ will converge to a torsion-free G_2 structure which is in the orbit of $\varphi$ under diffeomorphisms isotopic to the identity.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4310/jdg/1552442608

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Balliol College
Role:
Author
ORCID:
0000-0002-0456-4538
Publisher:
International Press Publisher's website
Journal:
Journal of Differential Geometry Journal website
Volume:
111
Issue:
3
Pages:
495-526
Publication date:
2019-03-13
Acceptance date:
2017-05-08
DOI:
EISSN:
1945-743X
ISSN:
0022-040x
Source identifiers:
968683
Pubs id:
pubs:968683
UUID:
uuid:00b6d397-c07b-4f1f-8ef2-c0afd5626b10
Local pid:
pubs:968683
Deposit date:
2019-02-04

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