We investigate the possibility of desingularizing a positively curved metric cone by an expanding gradient Ricci soliton with positive curvature operator. This amounts to study the deformation of such geometric structures. As a consequence, we prove that the moduli space of conical positively curved gradient Ricci expanders is connected.

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1 Alix DeruelleWe characterize complete nonnegatively curved steady gradient soliton with curvature in L 1 . We show that there are isometric to a product ((R 2 , g cigar ) × (R n−2 , eucl))/Γ where Γ is a Bieberbach group of rank n − 2. We prove also a similar local splitting result under weaker curvature assumptions.