Compactness of conformal metrics with integral bounds on curvature
Matthew J. Gursky
Source: Duke Math. J. Volume 72, Number 2
(1993), 339-367.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077289423
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References
[BPY] R. Brooks, P. Perry, and P. Yang, Isospectral sets of conformally equivalent metrics, Duke Math. J. 58 (1989), no. 1, 131–150.
Mathematical Reviews (MathSciNet): MR90i:58193
Zentralblatt MATH: 0667.53037
Digital Object Identifier: doi:10.1215/S0012-7094-89-05808-0
Project Euclid: euclid.dmj/1077307376
[CY1] S.-Y. A. Chang and P. Yang, Compactness of isospectral conformal metrics on $S\sp 3$, Comment. Math. Helv. 64 (1989), no. 3, 363–374.
Mathematical Reviews (MathSciNet): MR90c:58181
Zentralblatt MATH: 0679.53038
Digital Object Identifier: doi:10.1007/BF02564682
[CY2] S.-Y. A. Chang and P. Yang, Isospectral conformal metrics on $3$-manifolds, J. Amer. Math. Soc. 3 (1990), no. 1, 117–145.
Mathematical Reviews (MathSciNet): MR91c:58140
Zentralblatt MATH: 0701.58056
Digital Object Identifier: doi:10.2307/1990985
JSTOR: links.jstor.org
[CY3] Sun-Yung A. Chang and Paul C. Yang, The conformal deformation equation and isospectral set of conformal metrics, Recent developments in geometry (Los Angeles, CA, 1987), Contemp. Math., vol. 101, Amer. Math. Soc., Providence, RI, 1989, pp. 165–178.
Mathematical Reviews (MathSciNet): MR90k:53072
Zentralblatt MATH: 0698.53024
[G] P. Gilkey, Leading terms in the asymptotics of the heat equation, Geometry of random motion (Ithaca, N.Y., 1987), Contemp. Math., vol. 73, Amer. Math. Soc., Providence, RI, 1988, pp. 79–85.
Mathematical Reviews (MathSciNet): MR89h:58199
Zentralblatt MATH: 0661.58034
[LP] J. Lee and T. Parker, The Yamabe problem, Bull. Amer. Math. Soc. (N.S.) 17 (1987), no. 1, 37–91.
Mathematical Reviews (MathSciNet): MR88f:53001
Zentralblatt MATH: 0633.53062
Digital Object Identifier: doi:10.1090/S0273-0979-1987-15514-5
Project Euclid: euclid.bams/1183553962
[LF] J. Lelong-Ferrand, Transformations conformes et quasiconformes des variétés riemanniennes; application à la démonstration d'une conjecture de A. Lichnerowicz, C. R. Acad. Sci. Paris Sér. A-B 269 (1969), A583–A586.
Mathematical Reviews (MathSciNet): MR40:7989
Zentralblatt MATH: 0201.09701
[MS] H. P. McKean, Jr. and I. M. Singer, Curvature and the eigenvalues of the Laplacian, J. Differential Geometry 1 (1967), no. 1, 43–69.
Mathematical Reviews (MathSciNet): MR36:828
Zentralblatt MATH: 0198.44301
Project Euclid: euclid.jdg/1214427880
[OPS1] B. Osgood, R. Phillips, and P. Sarnak, Extremals of determinants of Laplacians, J. Funct. Anal. 80 (1988), no. 1, 148–211.
Mathematical Reviews (MathSciNet): MR90d:58159
Zentralblatt MATH: 0653.53022
Digital Object Identifier: doi:10.1016/0022-1236(88)90070-5
[OPS2] B. Osgood, R. Phillips, and P. Sarnak, Compact isospectral sets of surfaces, J. Funct. Anal. 80 (1988), no. 1, 212–234.
Mathematical Reviews (MathSciNet): MR90d:58160
Zentralblatt MATH: 0653.53021
Digital Object Identifier: doi:10.1016/0022-1236(88)90071-7
[P] S. Peters, Convergence of Riemannian manifolds, Compositio Math. 62 (1987), no. 1, 3–16.
Mathematical Reviews (MathSciNet): MR88i:53076
Zentralblatt MATH: 0618.53036
[S1] R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984), no. 2, 479–495.
Mathematical Reviews (MathSciNet): MR86i:58137
Zentralblatt MATH: 0576.53028
Project Euclid: euclid.jdg/1214439291
[S2] R. Schoen, Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, Topics in calculus of variations (Montecatini Terme, 1987), Lecture Notes in Math., vol. 1365, Springer-Verlag, Berlin, 1989, pp. 120–154.
Mathematical Reviews (MathSciNet): MR90g:58023
Zentralblatt MATH: 0702.49038
Digital Object Identifier: doi:10.1007/BFb0089180
[SY] R. Schoen and S.-T. Yau, Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math. 92 (1988), no. 1, 47–71.
Mathematical Reviews (MathSciNet): MR89c:58139
Zentralblatt MATH: 0658.53038
Digital Object Identifier: doi:10.1007/BF01393992
[T] N. Trudinger, Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa (3) 22 (1968), 265–274.
Mathematical Reviews (MathSciNet): MR39:2093
Zentralblatt MATH: 0159.23801
[W] J. Wolf, Spaces of constant curvature, McGraw-Hill Book Co., New York, 1967.
Mathematical Reviews (MathSciNet): MR36:829
Zentralblatt MATH: 0162.53304
[Y] H. Yamabe, On a deformation of Riemannian structures on compact manifolds, Osaka Math. J. 12 (1960), 21–37.
Mathematical Reviews (MathSciNet): MR23:A2847
Zentralblatt MATH: 0096.37201
[Yg] D. Yang, $L^p$ pinching and compactness theorems for compact Riemannian manifolds, preprint.
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