Title: Laplacian solitons: questions and homogeneous examples,
Abstract: We give the first examples of closed Laplacian solitons which are shrinking,
and in particular produce closed Laplacian flow solutions with a finite-time
singularity. Extremally Ricci pinched G2-structures (introduced by Bryant)
which are steady Laplacian solitons have also been found. All the examples are
left-invariant G2-structures on solvable Lie groups.