Type II singularities on complete non-compact Yamabe flow

Abstract

<jats:title>Abstract</jats:title> <jats:p>This work concerns with the existence and detailed asymptotic analysis of type II singularities for solutions to complete non-compact conformally flat Yamabe flow with cylindrical behavior at infinity. We provide the specific blow-up rate of the maximum curvature and show that the solution converges, after blowing-up around the curvature maximum points, to a rotationally symmetric steady soliton. It is the first time that the steady soliton is shown to be a finite time singularity model of the Yamabe flow.</jats:p>