8.3 Geodesic loop

Consider a solution with asymptotics of the form of Equations (37View Equation) – (38View Equation) and va(𝜃) > 0. Then Q (τ,𝜃) converges and P (τ,𝜃) tends to infinity as τ → ∞. In other words, for a fixed 𝜃, the solution roughly speaking goes to the boundary along a geodesic in hyperbolic space; see Equation (21View Equation). Since P and Q, for a fixed τ, define a loop in hyperbolic space, the solution is asymptotically approximated by a “loop of geodesics”.
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