References
Ambrosetti, A., Malchiodi, A.: A multiplicity result for the Yamabe problem on S n. J. Funct. Anal. 168, 529–561 (1999)
Aubin, T.: Équations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire. J. Math. Pures Appl., IX. Sér. 55, 269–296 (1976)
Bartnik, R.: The mass of an asymptotically flat manifold. Commun. Pure Appl. Math. 39, 661–693 (1986)
Besse, A.L.: Einstein Manifolds. Springer, Berlin (1987)
Brendle, S.: Convergence of the Yamabe flow for arbitrary initial energy. J. Differ. Geom. 69, 217–278 (2005)
Brendle, S.: Blow-up phenomena for the Yamabe equation. J. Am. Math. Soc. (to appear)
Chow, B.: The Yamabe flow on locally conformally flat manifolds with positive Ricci curvature. Commun. Pure Appl. Math. 45, 1003–1014 (1992)
Druet, O., Hebey, E.: Elliptic equations of Yamabe type. Int. Math. Res. Surv. 1, 1–113 (2005)
Hebey, E., Vaugon, M.: Le problème de Yamabe équivariant. Bull. Sci. Math. 117, 241–286 (1993)
Lee, J.M., Parker, M.: The Yamabe problem. Bull. Am. Math. Soc. 17, 37–91 (1987)
Lohkamp, J.: The higher dimensional positive mass theorem I. Preprint (2006)
Schoen, R.M.: Conformal deformation of a Riemannian metric to constant scalar curvature. J. Differ. Geom. 20, 479–495 (1984)
Schoen, R.M.: A report on some recent progress on nonlinear problems in geometry. In: Surveys in Differential Geometry, pp. 201–241. Lehigh University, Bethlehem, PA (1991)
Schoen, R.M., Yau, S.T.: On the proof of the positive mass conjecture in general relativity. Commun. Math. Phys. 65, 45–76 (1979)
Schoen, R.M., Yau, S.T.: Lectures on Differential Geometry. International Press, Cambridge, MA (1994)
Schwetlick, H., Struwe, M.: Convergence of the Yamabe flow for large energies. J. Reine Angew. Math. 562, 59–100 (2003)
Taylor, M.: Partial Differential Equations, III. Applied Mathematical Sciences, vol. 117. Springer, New York (1997)
Witten, E.: A new proof of the positive energy theorem. Commun. Math. Phys. 80, 381–402 (1981)
Ye, R.: Global existence and convergence of the Yamabe flow. J. Differ. Geom. 39, 35–50 (1994)
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Brendle, S. Convergence of the Yamabe flow in dimension 6 and higher. Invent. math. 170, 541–576 (2007). https://doi.org/10.1007/s00222-007-0074-x
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DOI: https://doi.org/10.1007/s00222-007-0074-x