We prove that torsion-free G2 structures are (weakly) dy- namically stable along the Laplacian flow for closed G2 structures. More precisely, given a torsion-free G2 structure ¯ ' on a compact 7-manifold M, the Laplacian flow with initial value in (¯ '), sufficiently close to ¯ ', will converge to a point in the Diff 0 (M)-orbit of ¯ '.

中文翻译：

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沿拉普拉斯流的无扭转 $\mathrm{G}_2$ 结构的稳定性

我们证明，对于闭合的 G2 结构，无扭转 G2 结构沿拉普拉斯流是（弱）动态稳定的。更准确地说，给定一个无扭 G2 结构 ¯ ' 在紧凑的 7 流形 M 上，初始值在 (¯ ') 中的拉普拉斯流，足够接近¯ '，将收敛到 Diff 0 (M) 中的点- ¯' 的轨道。