Bulletin of the American Mathematical Society

Author(s): John M. Lee; Thomas H. Parker
Journal: Bull. Amer. Math. Soc. 17 (1987), 37-91.
MSC (1980): Primary 53A30; Secondary 35J20, 35J60
MathSciNet review: 888880
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[ADM1] R. Arnowitt, S. Deser, and C. Misner, Canonical variables for general relativity, Phys. Rev. 117 (1960), 1595-1602. MR 113668

[ADM2] R. Arnowitt, S. Deser, and C. Misner, Energy and the criteria for radiation in general relativity, Phys. Rev. 118 (1960), 1100-1104. MR 127945

[ADM3] R. Arnowitt, S. Deser, and C. Misner, Coordinate invariance and energy expressions in general relativity, Phys. Rev. 122 (1961), 997-1006. MR 127946

[A1] T. Aubin, Problèmes isopérimétriques et espaces de Sobolev, J. Diff. Geom. 11 (1976), 533-598. MR 448404

[A2] T. Aubin, Équations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, J. Math. Pures Appl. 55 (1976), 269-296. MR 431287

[A3] T. Aubin, Nonlinear analysis on manifolds. Monge-Ampère equations, Springer-Verlag, New York, 1982. MR 681859

[AM] P. Aviles and R. McOwen, Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds, preprint. MR 925121

[B] R. Bartnik, The mass of an asymptotically flat manifold, Comm. Pure Appl. Math. 34 (1986), 661-693. MR 849427

[BL] H. Brezis and E. Lieb, A relation between pointwise convergence of functions and convergence of functional, Proc. Amer. Math. Soc. 88 (1983), 486-490. MR 699419

[BN] H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 437-477. MR 709644

[C] M. Cantor, Elliptic operators and the decomposition of tensor fields, Bull. Amer. Math. Soc. (N.S.) 5 (1981), 235-262. MR 628659

[CSCB] A. Chaljub-Simon and Y. Choquet-Bruhat, Problèmes elliptiques du second ordre sur une variété euclidienne à l'infini, Ann. Fac. Sci. Toulouse 1 (1978), 9-25. MR 533596

[CBC] Y. Choquet-Bruhat and D. Christodoulou, Elliptic systems in H, Acta Math. 146 (1981), 129-150. MR 594629

[E] L. Eisenhart, Riemannian geometry, Princeton University Press, Princeton, N. J., 1926. MR 35081

[GHP] G. Gibbons, S. Hawking, and M. Perry, Path integrals and the indefiniteness of the gravitational action, Nucl. Phys. 8138 (1978), 141-150. MR 496312

[GT] D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, New York, 1983. MR 737190

[G] R. Graham, A conformal normal form, in preparation.

[HE] S. Hawking and S. Ellis, The large scale structure of space-time, Cambridge University Press, Cambridge, 1973. MR 424186

[JL1] D. Jerison and J. Lee, A subelliptic, nonlinear eigenvalue problem and scalar curvature on CR manifolds, Contemp. Math. 27 (1984), 57-63. MR 741039

[JL2] D. Jerison and J. Lee, The Yamabe problem on CR manifolds, J. Diff. Geom. 25 (1987) (to appear). MR 880182

[JL3] D. Jerison and J. Lee, Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem, J. Amer. Math. Soc. 1 (1988) (to appear). MR 924699

[JL4] D. Jerison and J. Lee, Intrinsic CR normal coordinates and the CR Yamabe problem, in preparation.

[K] J. Kazdan, Some applications of partial differential equations to problems in geometry, Surveys in Geometry, Japan, 1983 (preprint).

[KN] S. Kobayashi and N. Nomizu, Foundations of differential geometry. I, Interscience, New York, 1963.

[L] P.-L. Lions, Applications de la méthode de concentration-compacité à l'existence de fonctions extremales, C. R. Acad. Sci. Paris 296 (1983), 645-648. MR 705681

[Lo] R. Lockhart, Fredholm properties of a class of elliptic operators on non-compact manifolds, Duke Math. J. 48 (1981), 289-312. MR 610188

[M] R. McOwen, Behavior of the Laplacian on weighted Sobolev spaces, Comm. Pure Appl. Math. 32 (1979), 783-795. MR 539158

[NW] L. Nirenberg and H. Walker, The null spaces of elliptic partial differential operators in R, J. Math. Anal. Appl. 42 (1973), 271-301. MR 320821

[O] M. Obata, The conjectures on conformal transformations of Riemannian manifolds, J. Diff. Geom. 6 (1971), 247-258. MR 303464

[PR] T. Parker and S. Rosenberg, Invariants of conformal Laplacians, J. Diff. Geom., to appear. MR 880183

[PT] T. Parker and C. Taubes, On Witten's proof of the positive energy theorem, Comm. Math. Phys. 84 (1982), 223-238. MR 661134

[SU] J. Sacks and K. Uhlenbeck, The existence of minimal 2-spheres, Ann. of Math. 113 (1981), 1-24. MR 604040

[S] R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Diff. Geom. 20 (1984), 479-495. MR 788292

[SY1] R. Schoen and S.-T. Yau, On the proof of the positive mass conjecture in general relativity, Comm. Math. Phys. 65 (1979), 45-76. MR 526976

[SY2] R. Schoen and S.-T. Yau, Proof of the positive action conjecture in quantum relativity, Phys. Rev. Lett. 42 (1979), 547-548.

[SY3] R. Schoen and S.-T. Yau, The energy and the linear momentum of space-times in general relativity, Comm. Math. Phys. 79 (1981), 47-51. MR 609227

[SY4] R. Schoen and S.-T. Yau, Proof of the positive mass theorem. II, Comm. Math. Phys. 79 (1981), 231-260. MR 612249

[SY5] R. Schoen and S.-T. Yau, The geometry and topology of manifolds of positive scalar curvature, in preparation.

[SY6] R. Schoen and S.-T. Yau, Conformally flat manifolds, Kleinian groups and scalar curvature (preprint). MR 931204

[Ta] G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976), 353-372. MR 463908

[T] N. Trudinger, Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa 22 (1968), 265-274. MR 240748

[We] S. Webster, Pseudohermitian structures on a real hypersurface, J. Diff. Geom. 13 (1978), 25-41. MR 520599

[Wy] D. Weiyue, On a conformally invariant elliptic equation on R, Comm. Math. Phys. 107 (1986), 331-335. MR 863646

[W] E. Witten, A new proof of the positive energy theorem, Comm. Math. Phys. 80 (1981), 381-402. MR 626707

[Y] H. Yamabe, On a deformation of Riemannian structures on compact manifolds, Osaka Math. J. 12 (1960), 21-37. MR 125546

[Yau] S.-T. Yau, Problem section, Seminar on Differential Geometry (S.-T. Yau, ed.), Princeton University Press, Princeton, N. J., 1982. MR 645728

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