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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  κ -non-collapsing theorem. We will use both of them to study finite-time singularities of general flows of G 2  structures.

Shi-type estimates and finite time singularities of flows of G 2 structures