3 0 Ja n 20 01 Hypersurfaces in H n and the space of its horospheres

A classical theorem, mainly due to Aleksandrov [Ale58] and Pogorelov [Pog73], states that any Riemannian metric on S 2 with curvature K > −1 is induced on a unique convex surface in H 3. A similar result holds with the induced metric replaced by the third fundamental form. We show that the same phenomenon happens with yet another metric on immersed surfaces… CONTINUE READING