A pointwise finite-dimensional reduction method for Einstein-Lichnerowicz-type systems: The six-dimensional case

We construct blowing-up solutions for smooth perturbations of a focusing Einstein-Lichnerowicz system on a closed 6-dimensional manifold. Our construction combines asymptotic analysis techniques with a finite-dimensional reduction approach, following the scheme of proof developed in Premoselli (2016). The blow-up examples constructed here highlight in particular the role of the coupling field in dimension 6.