Stability of torsion-free G_2 structures along the Laplacian flow
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 $\varphi$ w...
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| Format: | Journal article |
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International Press
2019
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| _version_ | 1826256535126278144 |
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| author | Lotay, J Wei, Y |
| author_facet | Lotay, J Wei, Y |
| author_sort | Lotay, J |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T18:03:45Z |
| format | Journal article |
| id | oxford-uuid:00b6d397-c07b-4f1f-8ef2-c0afd5626b10 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:03:45Z |
| publishDate | 2019 |
| publisher | International Press |
| record_format | dspace |
| spelling | oxford-uuid:00b6d397-c07b-4f1f-8ef2-c0afd5626b102022-03-26T08:30:59ZStability of torsion-free G_2 structures along the Laplacian flowJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:00b6d397-c07b-4f1f-8ef2-c0afd5626b10Symplectic Elements at OxfordInternational Press2019Lotay, JWei, YWe 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. |
| spellingShingle | Lotay, J Wei, Y Stability of torsion-free G_2 structures along the Laplacian flow |
| title | Stability of torsion-free G_2 structures along the Laplacian flow |
| title_full | Stability of torsion-free G_2 structures along the Laplacian flow |
| title_fullStr | Stability of torsion-free G_2 structures along the Laplacian flow |
| title_full_unstemmed | Stability of torsion-free G_2 structures along the Laplacian flow |
| title_short | Stability of torsion-free G_2 structures along the Laplacian flow |
| title_sort | stability of torsion free g 2 structures along the laplacian flow |
| work_keys_str_mv | AT lotayj stabilityoftorsionfreeg2structuresalongthelaplacianflow AT weiy stabilityoftorsionfreeg2structuresalongthelaplacianflow |