Curvature pinching estimate under the Laplacian G_{2} flow
arXiv:2307.14289 · doi:10.1016/j.jfa.2025.111199
Abstract
In this paper, we derive a pinching estimate on the traceless Ricci curvature in term of scalar curvature and the C^{1} norm of the Weyl tensor under the Laplacian G_{2} flow for closed G_{2} structures. Then we apply this estimate to study the long time existence of the Laplacian G_{2} flow and prove that the C^{1} norm of the Weyl tensor has to blow up at least at a certain rate under bounded scalar curvature.
24 pages