Rigidity of compact ideal boundaries of manifolds joined by Hausdorff approximations (Q1345350)

For a Hadamard manifold \(M\) or a manifold \(M\) of asymptotically nonnegative curvature the ideal boundary \(M(\infty)\) of \(M\) with its Tits metric \(Td\) is defined. The author shows that \((M(\infty),Td)\) and \((N(\infty),Td)\) are isometric if there is a Hausdorff approximation from \(M\) to \(N\) and if either 1) \(M\) and \(N\) are Hadamard manifolds and \((M(\infty),Td)\) and \((N(\infty),Td)\) are compact or 2) \(M\) and \(N\) have asymptotically nonnegative curvature. Moreover he gives an example of two asymptotically flat surfaces with isometric ideal boundaries which do not admit any Hausdorff approximation.