Compact domains with prescribed convex boundary metrics in quasi-Fuchsian manifolds
classification
🧮 math.MG
keywords
boundarycompactconvexmetricprescribedquasi-fuchsianalexandrovcoincides
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We show the existence of a convex compact domain in a quasi-Fuchsian manifold such that the induced metric on its boundary coincides with a prescribed surface metric of curvature $K\geq-1$ in the sense of A. D. Alexandrov.
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