Beltrami-Courant Differentials and $G_{\infty}$-algebras
  Using the symmetry properties of two-dmensional sigma models, we introduce a notion of the Beltrami-Courant differential, so that there is a natural homotopy Gerstenhaber algebra related to it. We conjecture that the generalized Maurer-Cartan equation for the corresponding $L_{\infty}$ subalgebra gives solutions to the Einstein equations. 
Anton M. Zeitlin
math.QA hep-th math-ph math.DG math.MP