Séance Séminaire

Séminaire Gaston Darboux

Extension of Möbius boundary homeomorphisms

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.