### 10.3 Interpretation of the asymptotic velocity as a rate of convergence to the boundary in hyperbolic
space

Similarly to the discussion carried out in the polarized case, the asymptotic velocity can be
interpreted as the rate at which the solution goes to the boundary of hyperbolic space; see
Equation (36). Given a solution , we shall let denote the hyperbolic distance from a
reference point to (the particular choice of reference point is not of importance).
Then
see [79, Theorem 1.2, p. 982].