Quantitative stability for Yamabe minimizers on manifolds with boundary

Key Points

• This research aims to investigate the quantitative stability of Yamabe-type minimizers on compact manifolds with boundary.
• Analyzed a Yamabe-type functional on compact manifolds with boundary.
• Focused on the relationship between the deficit and distance to the minimizing set.
• Reduced the problem to an analogous question involving an effective functional on the boundary.
• Demonstrated that the deficit controls the distance to the minimizing set effectively.
• Established results that connect the behaviors of the functional and boundary metrics.