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.