Shi-type estimates and finite time singularities of flows of G${}_2$ structures

Abstract

In this paper, we extend Lotay-Wei's Shi-type estimate from Laplacian flow to more general flows of G${}_2$ structures including the modified Laplacian co-flow. Then we prove a version of $\kappa$-non-collapsing theorem. We will use both of them to study finite time singularities of general flows of G${}_2$ structures.

The previous version is too short. So it is merged into a new paper

References in corpus (2)

• Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior
• On the conditions to extend Ricci flow(II)

Cited by in corpus (8)

• Hypersymplectic 4-manifolds, the $G_2$-Laplacian flow and extension assuming bounded scalar curvature
• Spacelike mean curvature flow
• Harmonic flow of geometric structures
• Flows of ${\mathrm{G}}_2$-structures on contact Calabi--Yau $7$-manifolds
• A report on the hypersymplectic flow
• Local derivative estimates for the heat equation coupled to the Ricci flow
• Curvature pinching estimate under the Laplacian G_{2} flow
• Real analyticity of the modified Laplacian coflow