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Hypersurfaces of constant curvature in Hyperbolic space

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arxiv 1010.4008 v1 pith:BBHABWMD submitted 2010-10-19 math.AP

Bo Guan (Ohio State University) , Joel Spruck (Johns Hopkins University) This is my paper
classification math.AP
keywords curvaturegammaconvexfunctionshyperbolichypersurfacessigmaasymptotic
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We show that for a very general and natural class of curvature functions, the problem of finding a complete strictly convex hypersurface satisfying f({\kappa}) = {\sigma} over (0,1) with a prescribed asymptotic boundary {\Gamma} at infinity has at least one solution which is a "vertical graph" over the interior (or the exterior) of {\Gamma}. There is uniqueness for a certain subclass of these curvature functions and as {\sigma} varies between 0 and 1, these hypersurfaces foliate the two components of the complement of the hyperbolic convex hull of {\Gamma}.

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  1. Curvature estimates for hypersurfaces of constant curvature in hyperbolic space II

    math.DG 2025-05 unverdicted novelty 5.0 of 10

    Derives curvature estimates to prove existence of smooth complete hypersurfaces in hyperbolic space with constant (n-2)-curvature and prescribed asymptotic boundary for the full range of curvature values.

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