Curvature pinching estimate under the Laplacian G_{2} flow

Chuanhuan Li; Yi Li

doi:10.1016/j.jfa.2025.111199

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arXiv · 2307.14289

Curvature pinching estimate under the Laplacian G_{2} flow

Chuanhuan Li·Yi Li

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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.

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BibTeX RIS

Chuanhuan Li, Yi Li. 2023-07-26. Curvature pinching estimate under the Laplacian G_{2} flow. https://doi.org/10.1016/j.jfa.2025.111199

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