Duke Mathematical Journal

Complete conformal metrics with negative scalar curvature in compact Riemannian manifolds

Patricio Aviles and Robert C. McOwen

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Article information

Source
Duke Math. J. Volume 56, Number 2 (1988), 395-398.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077306601

Digital Object Identifier
doi:10.1215/S0012-7094-88-05616-5

Mathematical Reviews number (MathSciNet)
MR932852

Zentralblatt MATH identifier
0645.53023

Subjects
Primary: 58G30
Secondary: 35J60: Nonlinear elliptic equations 53A30: Conformal differential geometry 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

Citation

Aviles, Patricio; McOwen, Robert C. Complete conformal metrics with negative scalar curvature in compact Riemannian manifolds. Duke Math. J. 56 (1988), no. 2, 395--398. doi:10.1215/S0012-7094-88-05616-5. http://projecteuclid.org/euclid.dmj/1077306601.


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References

  • [1] P. Aviles, A study of the singularities of solutions of a class of nonlinear elliptic partial differential equations, Comm. Partial Differential Equations 7 (1982), no. 6, 609–643.
  • [2] P. Aviles and R. McOwen, Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds, to appear in J. differential Geom.
  • [3] C. Loewner and L. Nirenberg, Partial differential equations invariant under conformal or projective transformations, Contributions to analysis (a collection of papers dedicated to Lipman Bers), Academic Press, New York, 1974, pp. 245–272.
  • [4] M. Protter and H. Weinberger, Maximum principles in differential equations, Prentice-Hall Inc., Englewood Cliffs, N.J., 1967.
  • [5] L. Véron, Singularités éliminables d'équations elliptiques non linéaires, J. Differential Equations 41 (1981), no. 1, 87–95.