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Graphs with prescribed mean curvature on hyperbolic spaces

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Abstract

We study a quasilinear elliptic equation in the unit ball ofℝ m. Using this result we get the existence of graphs with prescribed curvature on hyperbolic spacesℍ m inℍ m ×ℝ.

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References

  1. Bombieri E., De Giorgi E. andGiusti E.,Minimal cones and the Bernstein problem. Invent. Math.7 243–268 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  2. Duc D.M. andHieu N.V.,Graphs with prescribed mean curvature on Poincaré disk. Preprint

  3. Duc D.M. andSalavessa I.M.C.,On a class of graphs with prescribed mean curvature. To appear on Manuscripta Mathematica

  4. Gilbarg D. andTrudinger N.Elliptic partial differential equations of sccond order. Springer-Verlag, Berlin, 1983

    Google Scholar 

  5. Hartman P.,On quasilinear clliptic functional-diffcrential equations, In: Differential equations and Dynamical systems, Proc. Internat. Sympos. Mayaguez, P.R., (1965), p. 393–407, Academic Press, New York, 1967

    Google Scholar 

  6. Ladyzhenskya O.A. andUral'tseva N.N.,Linear and quasilinear elliptic equations. Academic Press, New-York, 1968

    Google Scholar 

  7. Moser J.,On Harnack's theorem for clliptic differential cquations. Comm. Pure and Applied Math.14 577–591 (1961)

    MATH  Google Scholar 

  8. Salavessa I.M.C.,Graphs with parallel mean curvature and a variational problem in conformal geometry. Ph.D. Thesis, Warwick, 1988

  9. Salavessa I.M.C. Graphs with parallel mean curvature. Proc. Amer. Math. Soc.107, 449–458 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  10. Simons J.,Minimal varieties in Riemannian manifolds. Ann. Math.88, 62–105 (1968)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Hochiminh City, 227 Nguyen Van Cu-Quan 5, Hochiminh City, Vietnam

    Duong Minh Duc & Nguyen Van Hieu

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  1. Duong Minh Duc
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  2. Nguyen Van Hieu
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Duc, D.M., Van Hieu, N. Graphs with prescribed mean curvature on hyperbolic spaces. Manuscripta Math 83, 111–121 (1994). https://doi.org/10.1007/BF02567603

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  • DOI: https://doi.org/10.1007/BF02567603

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