Local curvature estimates for the Laplacian flow

Abstract In this paper we give local curvature estimates for the Laplacian flow on closed $$G_{2}$$ G 2 -structures under condition that Ricci is bounded along flow. The main ingredient consists of idea Kotschwar et al. (J Funct Anal 271(9):2604–2630, 2016) who gave complete manifolds and then provided a new elementary proof Sesum’s result (Sesum in Am J Math 127(6):1315–1324, 2005), particular structure -structures. As an immediate consequence, Lotay Wei’s (Geom 27(1):165–233, 2017) which analogue theorem. second about interesting evolution equation scalar Roughly speaking, can prove time derivative $$R_{g(t)}$$ R g ( t ) equal to , plus extra term be written as difference two nonnegative quantities.