Quantitative stability for Yamabe minimizers on manifolds with boundary

Abstract This paper addresses the quantitative stability for a Yamabe‐type functional on compact manifolds with boundary introduced by Escobar. Minimizers of the functional correspond to scalar‐flat metrics with constant mean curvature on the boundary. We prove that the deficit controls the distance to the minimizing set to a suitable power by reducing the problem to the analogous question for an effective functional on the boundary.