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A compact Fuchsian manifold with boundary is a hyperbolic 3-manifold homeomorphic to $S_g \times [0; 1]$ such that the boundary component $S_g \times \{ 0\}$ is geodesic. We prove that… Click to show full abstract
A compact Fuchsian manifold with boundary is a hyperbolic 3-manifold homeomorphic to $S_g \times [0; 1]$ such that the boundary component $S_g \times \{ 0\}$ is geodesic. We prove 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.
Keywords:
fuchsian manifolds;
rigidity compact;
convex boundary;
manifolds convex;
compact fuchsian
Journal Title: International Mathematics Research Notices
Year Published: 2021
Link to full text (if available)
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Journal Title: International Mathematics Research Notices
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!