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Conformally flat manifolds, Kleinian groups and scalar curvature

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References

  • [AM] Adams, D.R., Meyers, N.G.: Bessel potentials, inclusion relations among classes of exceptional sets. Indiana Univ. Math. J.22, 873–905 (1973)

    Google Scholar 

  • [Au] Aubin, T.: Équations différentielles nonlinéaires et Problem de Yamabe concernant la courbure scalaire. J. Math. Pure Appl.55, 269–296 (1976)

    Google Scholar 

  • [B] Brooks, R.: The fundamental group and the spectrum of the Laplacian. Comm. Math. Helv.56, 581–598 (1981)

    Google Scholar 

  • [CG] Cheeger, J., Gromoll, D.: The splitting theorem for manifolds of nonnegative Ricci curvature. J. Differ. Geom.6, 119–128 (1971)

    Google Scholar 

  • [CY] Cheng, S.Y., Yau, S.-T.: Differential equation on Riemannian manifolds and their geometric application. Comm. Pure Appl. Math.28, 333–354 (1975)

    Google Scholar 

  • [F] Fried, D.: Closed similarity manifolds. Comm. Math. Helv.55, 576–582 (1980)

    Google Scholar 

  • [G] Goldman, W.M.: Conformally flat manifolds with nilpotent holonomy and the uniformization problem for 3-manifolds. Trans. Am. Math. Soc.278, 573–583 (1983)

    Google Scholar 

  • [Ka] Kamishima, Y.: Conformally flat manifolds whose development maps are not surjective I (Preprint)

  • [Ku1] Kuiper, N.: On conformally flat manifolds in the large. Ann. Math.50, 916–924 (1949)

    Google Scholar 

  • [Ku2] Kuiper, N.: On compact conformally euclidean spaces of dimension >2. Ann. Math.52, 478–490 (1950)

    Google Scholar 

  • [LN] Loewner, C., Nirenberg, L.: Partial differential equations invariant under conformal or projective transformations. Contribution to Analysis, 245–272. Academic Press, New York 1974

    Google Scholar 

  • [M] Morrey, C.B.: Multiple Integrals in the Calculus of Variations, Springer, New York, 1966

    Google Scholar 

  • [P] Patterson, S.J.: The limit set of a Fuchsian group. Acta Math.136, 241–273 (1976)

    Google Scholar 

  • [Sc1] Schoen, R.: Conformal deformation of a Riemannian metric to constant scalar curvature. J. Differ. Geom.20, 479–495 (1984)

    Google Scholar 

  • [Sc2] Schoen, R.: The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation (to appear in Comm. Pure Appl. Math., 1988)

  • [Sp] Spivak, M.: A Comprehensive Introduction to Differential Geometry, Volume Four, Publish or Perish, Inc., Berkeley, 1979

    Google Scholar 

  • [SY1] Schoen, R., Yau, S.-T.: On the proof of the positive mass conjecture in general relativity. Comm. Math. Phys.65, 45–76 (1979)

    Google Scholar 

  • [SY2] Schoen, R., Yau, S.-T.: Proof of the positive mass theorem II. Comm. Math. Phys.79, 231–260 (1981)

    Google Scholar 

  • [Su] Sullivan, D.: The density at infinity of a discrete group of hyperbolic motions. IHES Publications Mathematiques No. 50, 171–202 (1979)

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Research supported in part by NSF grant #DMS84-09447 and ONR contract #N-00014-85-K-0367

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Schoen, R., Yau, S.T. Conformally flat manifolds, Kleinian groups and scalar curvature. Invent Math 92, 47–71 (1988). https://doi.org/10.1007/BF01393992

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