Skip to main content
SpringerLink
Log in

Radial Graphs with Constant Mean Curvature in the Hyperbolic Space

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

The existence is proved of radial graphs with constant mean curvature in the hyperbolic space Hn+1 defined over domains in geodesic spheres of Hn+1 whose boundary has positive mean curvature with respect to the inward orientation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Barbosa, J. L. and Earp, R. S.: Prescribed mean curvature hypersurfaces in ℍn+1 with convex planar boundary I, Preprint (1996).

  2. Barbosa, J. L. and Earp, R. S.: Prescribed mean curvature hypersurfaces in ℍn+1 (−1)with convex planar boundary, I, Geom. Dedicata 71 (1998), 61–74.

    Google Scholar 

  3. Gilbarg, D. and Trudinger, N.: Elliptic Partial Differential Equations of Second Order, 2nd edn, Springer-Verlag, Berlin, 1997.

    Google Scholar 

  4. López, R.: Graphs of constant mean curvature in hyperbolic space, Preprint (1999).

  5. López, R. and Montiel, S.: Existence of constant mean curvature graphs in hyperbolic space, Calc. Var. Partial Differential Equations 8 (1999), 177–190.

    Google Scholar 

  6. Morrey, Jr., C. B.: Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin, 1966.

    Google Scholar 

  7. Nelli, B., Hypersurfaces de courbure constante dans l'espace hyperbolique, Thése de Doctorat, Paris VII (1995).

    Google Scholar 

  8. Nelli, B. and Spruck, J.: On the existence and uniqueness in hyperbolic space of constant mean curvature hypersurfaces in hyperbolic space, In: J. Jost (ed.), Geometric Analysis and the Calculus Variations, International Press, Cambridge, 1996, pp. 253–266.

    Google Scholar 

  9. Serrin, J.: The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables, Philos. Trans. Royal Soc. London Ser A 264 (1969), 413–496.

    Google Scholar 

  10. Treibergs, A. and Wei, W.: Embedded hyperspheres with prescribed mean curvature, J. Differential Geom. 18 (1983), 513–521.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Ceará, 60455-670, Fortaleza-Ce, Brazil

    Jorge Herbert S. De Lira

Authors
  1. Jorge Herbert S. De Lira
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

De Lira, J.H.S. Radial Graphs with Constant Mean Curvature in the Hyperbolic Space. Geometriae Dedicata 93, 11–23 (2002). https://doi.org/10.1023/A:1020302128556

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020302128556

Search

Navigation