Asymptotically Hyperbolic Manifolds with Boundary Conjugate Points but no Interior Conjugate Points

Stability Estimates for the X-Ray Transform on Simple Asymptotically Hyperbolic Manifolds

“…they contain no trapped geodesics) and they have no boundary conjugate points, that is, there exists no non-trivial Jacobi field Y along any unit-speed geodesic such that lim t→±∞ |Y (t)| g → 0. Using work of Knieper in [Kni18], the authors in [GGS + 19] showed that on a simple AH manifold there exist no interior conjugate points in the usual sense, whereas in [EG20] it was shown that non-trapping AH manifolds with no conjugate points in the usual sense may have boundary conjugate points, i.e. they are not simple in general.…”