Rigidity of compact Fuchsian manifolds with convex boundary

Abstract: By a compact Fuchsian manifold with boundary we mean a hyperbolic 3-manifold homeomorphic to $S_g \times [0; 1]$ such that the boundary component $S_g \times \{ 0\}$ is geodesic. Here $S_g$ is a closed oriented surface of genus $g>1$. Fuchsian manifolds are known as toy cases in the study of geometry of hyperbolic 3-manifolds with boundary. In my talk I will sketch a proof that a compact Fuchsian manifold with convex boundary is uniquely determined by the induced path metric on $S_g \times \{1\}$. We do not put further restrictions on the boundary except convexity. This unifies two previously known results: in the case of smooth boundary such a result follows from a work of Schlenker and in the case of polyhedral boundary it was proven by Fillastre.

differential geometry

Audience: researchers in the topic

Pangolin seminar

Series comments: TIME HAS CHANGED: 15:30 Paris 10:30AM Rio de Janeiro

Description: Differential geometry seminar

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