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Hypersurfaces of Constant Curvature in Hyperbolic Space I

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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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Authors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, OH, 43210, USA

    Bo Guan

  2. Department of Mathematics, Johns Hopkins University, Baltimore, MD, 21218, USA

    Joel Spruck

  3. 805-D Runaway Bay Ln, Mount Pleasant, SC, 29464, USA

    Marek Szapiel

Authors
  1. Bo Guan
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  2. Joel Spruck
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  3. Marek Szapiel
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Corresponding author

Correspondence to Joel Spruck.

Additional information

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

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