An asymptotically hyperbolic manifold is a Riemannian manifold whose metric approaches a hyperbolic reference metric on its ends. In
the spherical-end convention for curvature 
, the reference metric is
 |
where 
is the unit round metric on 
. Writing 
, one differentiated convention requires 
for the prescribed derivative orders and some 
. The rate, regularity, and end geometry must be specified
for a mass theorem.
