Skip to main content
Log in

On the Dirichlet problem for minimal graphs in hyperbolic space

  • Published:
Inventiones mathematicae Aims and scope

An Erratum to this article was published on 29 November 2011

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

References

  • [An 1] Anderson, M.: Complete minimal varieties in hyperbolic space. Invent Math.69, 477–494 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  • [An 2] Anderson, M.: Complete minimal hypersurfaces in hyperbolicn-manifolds. Comment. Math. Helv.58, 264–290 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  • [GT] Gilberg, D., Trudinger, N.: Elliptic partial differential equations of second order. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  • [HL] Hardt, R., Lin, F.H.: Regularity at infinity for area-minimizing hypersurfaces in hyperbolic space. Invent. Math.88, 217–224 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  • [KN] Kohn, J.J., Nirenberg, L.: Degenerated elliptic-parabolic equations of second order. Commun. Pure Appl. Math.20, 797–872 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  • [L] Lin, F.H.: Regularity for a class of parametric obstacle problems. Ph.D. Thesis (July 1985), Univ. of Minnesota, Minneapolis

  • [L2] Lin, F.H.: Asymptotic behavior of complete area-minimizing currents in hyperbolic space. To appear in CPAM (1989)

  • [LL] Lau, C.P., Lin, F.H.: The best Holder exponent for non-parametric least area problem. Ind. Univ. Math. J.4, 809–813 (1985)

    Article  MathSciNet  Google Scholar 

  • [MN] Morrey, C.B., Nirenberg, L.: On the analyticity of the solutions of linear elliptic systems of partial differential equations. Commun Pure Appl. Math.10, 271–290 (1957)

    Article  MATH  MathSciNet  Google Scholar 

  • [SL 1] Simon, L.: Boundary regularity for solutions of the non-parametric least area problem. Ann. Math.103, 429–455 (1976)

    Article  MATH  Google Scholar 

  • [SL 2] Simon, L.: Boundary behavior of solutions of the non-parametric least area problem. Aust. Math. Bull26, 17–27 (1982)

    Article  MATH  Google Scholar 

  • [SU] Sachs, J., Uhlenbeck, K.: Minimal immersion of Riemann surfaces in Riemannian manifold. Trans. Am. Math. Soc.271, 639–652 (1982)

    Article  Google Scholar 

  • [SY] Schoen, R., Yau, S.T.: Existence of incompressible minimal surfaces and the topology of 3-manifolds with non-negative scalar curvature. Ann. Math.110, 127–142 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  • [U] Uhlenbeck, K.: Closed minimal surfaces in hyperbolic 3-manifolds. In: “Siminar on minimal submanifolds, Bombieri, E. (ed.) Ann. Math. Studies103, 147–168 (1983)

  • [W] Williams, G.: The Dirichlet problem for the minimal surface equations with Lipschitz continuous boundary data. CMA-R-41-83 Australian National Univ. See also CMA-R01-84

Download references

Author information

Authors and Affiliations

Authors

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s00222-011-0370-3

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lin, F.H. On the Dirichlet problem for minimal graphs in hyperbolic space. Invent Math 96, 593–612 (1989). https://doi.org/10.1007/BF01393698

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01393698

Keywords

Navigation