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 $\phi$ on a compact 7-manifold, the Laplacian flow with initial value cohomologous and sufficiently close to $\phi$ will converge to a torsion-free G_2 structure which is in the orbit of $\phi$ under diffeomorphisms isotopic to the identity.

28 pages, v2: minor corrections and additions, accepted version for JDG

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