Stability of torsion-free G2 structures along the Laplacian flow

Jason D. Lotay University of Oxford Yong Wei Australian National University

Differential Geometry mathscidoc:1908.10006

Journal of Differential Geometry, 111, (3), 495-526, 2019.3
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, the Laplacian flow with initial value cohomologous and sufficiently close to φ will converge to a torsion-free G2 structure which is in the orbit of φ under diffeomorphisms isotopic to the identity. We deduce, from fundamental work of Joyce [18], 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.
Laplacian flow, G2 structure, torsion-free, stability
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@inproceedings{jason2019stability,
  title={Stability of torsion-free G2 structures along the Laplacian flow},
  author={Jason D. Lotay, and Yong Wei},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190819180643063978413},
  booktitle={Journal of Differential Geometry},
  volume={111},
  number={3},
  pages={495-526},
  year={2019},
}
Jason D. Lotay, and Yong Wei. Stability of torsion-free G2 structures along the Laplacian flow. 2019. Vol. 111. In Journal of Differential Geometry. pp.495-526. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190819180643063978413.
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