Slowly converging Yamabe-type flow on manifolds with boundary

Carlotto, Chodosh and Rubinstein studied the rate of convergence of the Yamabe flow on a closed (compact without boundary) manifold M: partial differential partial differential tg(t) = -(Rg(t) -R over bar g(t))g(t)inM. In this paper, we prove the corresponding results on manifolds with boundary. More precisely, given a compact manifold M with smooth boundary partial differential M, we study the convergence rate of the Yamabe flow with boundary: partial differential partial differential tg(t) = -(Rg(t) -R over bar g(t))g(t)inMandHg(t) = 0on partial differential M and the conformal mean curvature flow: partial differential partial differential tg(t) = -(Hg(t) -H over bar g(t))g(t)on partial differential MandRg(t) = 0inM.