Linear stability of homogeneous Ricci solitons

Abstract

As a step towards understanding the analytic behavior of type-III Ricci flow singularities, that is, immortal solutions that exhibit |Rm| ≤ C/t curvature decay, we examine the linearization of an equivalent flow at fixed points discovered recently by Baird, Danielo, and Lott: nongradient homogeneous expanding Ricci solitons on nilpotent or solvable Lie groups. For all explicitly known nonproduct examples, we demonstrate linear stability of the flow at these fixed points and prove that the linearizations generate C0 semigroups.