Curvature pinching estimate under the Laplacian G_{2} flow

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.

arXiv comment24 pages

References in corpus (19)

• On Type I Singularities in Ricci flow
• Flows of G_2 Structures, I
• Deformations of G_2 and Spin(7) Structures on Manifolds
• Laplacian flow for closed G_2 structures: Shi-type estimates, uniqueness and compactness
• Short-time behaviour of a modified Laplacian coflow of G2-structures
• Curvature decomposition of G_2 manifolds
• Stability of torsion-free G_2 structures along the Laplacian flow
• Hypersymplectic 4-manifolds, the $G_2$-Laplacian flow and extension assuming bounded scalar curvature
• Shi-type estimates and finite time singularities of flows of G${}_2$ structures
• Laplacian Solitons and Symmetry in G_2-geometry
• Laplacian flow for closed G_2 structures: real analyticity
• Cohomogeneity-one $G_2$-Laplacian flow on 7-torus
• Modified Laplacian coflow of $G_2$-structures on manifolds with symmetry
• A class of eternal solutions to the G${}_2$-Laplacian flow
• Flows of ${\mathrm{G}}_2$-structures on contact Calabi--Yau $7$-manifolds
• Introduction to ${\mathrm{G}}_2$ geometry
• Flows of $G_2$-structures, II: Curvature, torsion, symbols, and functionals
• Gradient estimates and parabolic frequency under the Laplacian G_2 flow
• Local curvature estimates along the $\kappa$-LYZ flow

Cited by in corpus (1)

• Real analyticity of the modified Laplacian coflow