Abstract
We investigate the problem of finding, in hyperbolic space, a complete strictly convex hypersurface which has a prescribed asymptotic boundary at infinity and which has some fixed curvature function being constant. Our results apply to a very general class of curvature functions.
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Research of the first and second authors was supported in part by NSF grants.
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Guan, B., Spruck, J. & Szapiel, M. Hypersurfaces of Constant Curvature in Hyperbolic Space I. J Geom Anal 19, 772–795 (2009). https://doi.org/10.1007/s12220-009-9086-7
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DOI: https://doi.org/10.1007/s12220-009-9086-7
Keywords
- Hypersurfaces of constant curvature
- Hyperbolic space
- Asymptotic boundary
- Fully nonlinear elliptic equations