A Bogovskiǐ-type operator for Corvino–Schoen hyperbolic gluing

Abstract

We construct a solution operator for the linearized constant scalar curvature equation at hyperbolic space in dimension larger than or equal to two. The solution operator has good support propagation properties and gains two derivatives relative to standard norms. It can be used for Corvino–Schoen-type hyperbolic gluing, partly extending the recently introduced Mao–Oh–Tao gluing method to the hyperbolic setting.