标题： 曲率压缩估计在拉普拉斯 G_{2}流下 显示英文标题

标题： Curvature pinching estimate under the Laplacian G_{2} flow

摘要： 在本文中，我们在闭合 G_{2}结构的 Laplacian G_{2}流下，根据标量曲率和 Weyl 张量的 C^{1}范数，推导出关于无迹 Ricci 曲率的压缩估计。然后我们将此估计应用于研究 Laplacian G_{2}流的长时间存在性，并证明在标量曲率有界的情况下，Weyl 张量的 C^{1}范数必须至少以一定的速率爆破。 显示英文摘要

摘要： 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.