Hyperbolic cusps with convex polyhedral boundary - Mathematics > Differential GeometryReportar como inadecuado




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Abstract: We prove that a 3-dimensional hyperbolic cusp with convex polyhedral boundaryis uniquely determined by the metric induced on its boundary. Furthemore, anyhyperbolic metric on the torus with cone singularities of positive curvaturecan be realized as the induced metric on the boundary of a convex polyhedralcusp. The proof uses the total scalar curvature functional on the space of``cusps with particles-, which are hyperbolic cone-manifolds with the singularlocus a union of half-lines. We prove, in addition, that convex polyhedralcusps with particles are rigid with respect to the induced metric on theboundary and the curvatures of the singular locus. Our main theorem isequivalent to a part of a general statement about isometric immersions ofcompact surfaces.



Autor: François Fillastre, Ivan Izmestiev IFM

Fuente: https://arxiv.org/







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