In this talk, I will review recent results of K. Biswas. It is an open problem whether
every Möbius homeomorphism between the visual boundaries of two Hadamard
manifolds of curvature at most -1 extends to an isometry between them. A positive
answer would resolve the long-standing marked length spectrum rigidity conjecture
of Burns-Katok for closed negatively curved manifolds. Biswas' results yield an
isometry between certain functorial thickenings of the manifolds, which lie within
uniformly bounded distance and can be identified with their injective hulls.