Curvature pinching estimate under the Laplacian G₂ flow

2023/07/26 by Chuanhuan Li, Yi Li, Li, Chuanhuan +1
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2307.14289

Abstract

In this paper, we derive a pinching estimate on the traceless Ricci curvature in term of scalar curvature and the C¹ norm of the Weyl tensor under the Laplacian G₂ flow for closed G₂ structures. Then we apply this estimate to study the long time existence of the Laplacian G₂ flow and prove that the C¹ norm of the Weyl tensor has to blow up at least at a certain rate under bounded scalar curvature.

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