Lotay, JD;
Wei, Y;
(2019)
Stability of torsion-free G_2 structures along the Laplacian flow.
Journal of Differential Geometry
, 111
(3)
pp. 495-526.
10.4310/jdg/1552442608.
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Abstract
We prove that torsion-free G2 structures are (weakly) dynamically stable along the Laplacian flow for closed G2 structures. More precisely, given a torsion-free G2 structure φ¯¯¯ on a compact 7-manifold M, the Laplacian flow with initial value in [φ¯¯¯], sufficiently close to φ¯¯¯, will converge to a point in the Diff0(M)-orbit of φ¯¯¯. We deduce, from fundamental work of Joyce, that the Laplacian flow starting at any closed G2 structure with sufficiently small torsion will exist for all time and converge to a torsion-free G2 structure.
| Type: | Article |
|---|---|
| Title: | Stability of torsion-free G_2 structures along the Laplacian flow |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4310/jdg/1552442608 |
| Publisher version: | http://doi.org/10.4310/jdg/1552442608 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Laplacian flow, G2 structure, torsion-free, stability |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10070158 |
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