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Prescription of Gauss curvature on compact hyperbolic orbifolds

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  • In this paper, we generalize a result by Alexandrov on the Gauss curvature prescription for Euclidean convex bodies. We prove an analogous result for hyperbolic orbifolds. In addition to the duality theory for convex sets, our main tool comes from optimal mass transport.
    Mathematics Subject Classification: Primary: 49Q20; Secondary: 52C07, 53C42.


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