Conformal geometry, contact geometry, and the calculus of variations
Jeff A. Viaclovsky
Source: Duke Math. J. Volume 101, Number 2 (2000), 283-316.
First Page PDF: View first page of article (PDF, 32 KB)Primary Subjects: 53C21
Secondary Subjects: 35J60, 49J10, 58E11
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1092749151
Mathematical Reviews number (MathSciNet):
MR1738176
Digital Object Identifier: doi:10.1215/S0012-7094-00-10127-5
Zentralblatt MATH identifier:
0990.53035
References
Melvin S. Berger, Nonlinearity and Functional Analysis: Lectures on Nonlinear Problems in Mathematical Analysis, Pure Appl. Math. 74, Academic Press, New York, 1977.
Mathematical Reviews (MathSciNet):
MR488101
Arthur L. Besse, Einstein Manifolds, Ergeb. Math. Grenzgeb. (3) 10, Springer-Verlag, Berlin, 1987.
Mathematical Reviews (MathSciNet):
MR867684
Robert Bryant, Phillip A. Griffiths, and Lucas Hsu, The Poincaré-Cartan form, Institute for Advanced Study preprint, 1997.
L. Caffarelli, L. Nirenberg, and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations, III: Functions of the eigenvalues of the Hessian, Acta Math. 155 (1985), 261--301.
Mathematical Reviews (MathSciNet):
MR806416
Digital Object Identifier: doi:10.1007/BF02392544
Élie Cartan, Les espaces à connexion conforme, Ann. Soc. Polon. Math. 2 (1923), 171--221.
Lars G\.arding, An inequality for hyperbolic polynomials, J. Math. Mech. 8 (1959), 957--965.
Mathematical Reviews (MathSciNet):
MR113978
Robert B. Gardner, A differential geometric generalization of characteristics, Comm. Pure Appl. Math. 22 (1969), 597--626.
Mathematical Reviews (MathSciNet):
MR255958
Digital Object Identifier: doi:10.1002/cpa.3160220504
I. M. Gelfand and S. V. Fomin, Calculus of Variations, rev. ed., Prentice-Hall, Englewood Cliffs, N.J., 1963.
Mathematical Reviews (MathSciNet):
MR160139
G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge Math. Lib., Cambridge Univ. Press, Cambridge, 1988.
Mathematical Reviews (MathSciNet):
MR944909
Shoshichi Kobayashi, Transformation Groups in Differential Geometry, Classics Math., Springer-Verlag, Berlin, 1995.
Mathematical Reviews (MathSciNet):
MR1336823
John M. Lee and Thomas H. Parker, The Yamabe problem, Bull. Amer. Math. Soc. (N.S.) 17 (1987), 37--91.
Mathematical Reviews (MathSciNet):
MR888880
Digital Object Identifier: doi:10.1090/S0273-0979-1987-15514-5
Project Euclid: euclid.bams/1183553962
Rafe Mazzeo, Daniel Pollack, and Karen Uhlenbeck, Moduli spaces of singular Yamabe metrics, J. Amer. Math. Soc. 9 (1996), 303--344.
Mathematical Reviews (MathSciNet):
MR1356375
Digital Object Identifier: doi:10.1090/S0894-0347-96-00208-1
Morio Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan 14 (1962), 333--340.
Mathematical Reviews (MathSciNet):
MR142086
--. --. --. --., The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geometry 6 (1971/72), 247--258.
Mathematical Reviews (MathSciNet):
MR303464
Project Euclid: euclid.jdg/1214430407
Richard S. Palais, The principle of symmetric criticality, Comm. Math. Phys. 69 (1979), 19--30.
Mathematical Reviews (MathSciNet):
MR547524
Digital Object Identifier: doi:10.1007/BF01941322
Project Euclid: euclid.cmp/1103905401
Robert C. Reilly, On the Hessian of a function and the curvatures of its graph, Michigan Math. J. 20 (1973), 373--383.
Mathematical Reviews (MathSciNet):
MR334045
Project Euclid: euclid.mmj/1029001155
Richard M. Schoen, ``Variational theory for the total scalar curvature functional for Riemannian metrics and related topics'' in Topics in Calculus of Variations (Montecatini Terme, 1987) Lecture Notes in Math. 1365, Springer-Verlag, Berlin, 1989, 120--154.
Mathematical Reviews (MathSciNet):
MR994021
Digital Object Identifier: doi:10.1007/BFb0089180
Jeff A. Viaclovsky, Conformally invariant Monge-Ampère equations: Global solutions, to appear in Trans. Amer. Math. Soc.
Mathematical Reviews (MathSciNet):
MR1694380
Digital Object Identifier: doi:10.1090/S0002-9947-00-02548-4
Xu Jia Wang, A class of fully nonlinear elliptic equations and related functionals, Indiana Univ. Math. J. 43 (1994), 25--54.
Mathematical Reviews (MathSciNet):
MR1275451
Digital Object Identifier: doi:10.1512/iumj.1994.43.43002
Duke Mathematical Journal