8.3 Geodesic loop
Consider a solution with asymptotics of the form of Equations (37) – (38) and
. Then
converges and
tends to infinity as
. In other words, for a fixed
, the solution
roughly speaking goes to the boundary along a geodesic in hyperbolic space; see Equation (21). Since
and
, for a fixed
, define a loop in hyperbolic space, the solution is asymptotically approximated by a
“loop of geodesics”.