This is a preview of subscription content, log in via an institution to check access.
References
Adams, D. R.,A sharp inequality of J. Moser for higher order derivatives. Annals of Math.,128 (1988), 385–398.
Aubin, T.,Fonction de Green et valeurs propres du Laplacien. J. Math. Pures et Appl.,53 (1974), 347–371.
Aubin, T.,Nonlinear Analysis on Manifolds. Monge—Ampere Equations. Springer Verlag, Berlin, 1982.
Berger, M. S.,On the conformal equivalence of compact 2-dimensional manifolds. J. Math. and Mech.,19 (1969), 13–18.
Berger, M. S.,Riemannian structures of prescribed Gaussian curvature for compact 2-manifolds. J. Differential Geometry,5 (1971), 325–332.
Berger, M., Gauduchon, P. andMazet, E.,Le Spectre d'une variété Riemannienne. Springer Verlag, LN, 194, Berlin, 1971.
Besse, A.,Einstein Manifolds, Springer Verlag, Berlin, 1987.
Bishop, R. L. andCrittenden, R. J.,Geometry of Manifolds. Academic Press, New York, 1964.
Branson, T., Chang, S-Y. A. andYang, P. C.,Estimates and extremals for zeta function determinants on four-manifolds. Preprint, UCLA, 1991.
Brézis, H. andWainger, S.,A note on limiting cases of Sobolev embeddings and convolution inequalities. Comm. Partial Diff. Eq.,5 (1980), 773–789.
Carleson, L andChang, S-Y. A.,On the existence of an extremal function for an inequality of J. Moser, Bull. Sc. Math.,110 (1986), 113–127.
Chang, S-Y andYang, P. C.,Conformal deformation of metrics on S 2. J. Differential Geometry,27 (1988), 259–296.
Cheeger, J. andEbin, D. G.,Comparison Theorems in Riemannian Geometry. North Holland, Amsterdam, 1975.
Cherrier, P.,Une Inégalité de Sobolev sur les variétés Riemanniennes. Bull. Sc. Math.,103 (1979), 353–374.
Cherrier, P.,Cas d'exception du théorème d'inclusion de Sobolev sur les variétés Riemanniennes et applications. Bull. Sc. math.,105 (1981) 235–288.
Cherrier, P.,Meilleurs constantes dans inégalités relatives aux espaces de Sobolev. Bull. Sc. Math.,108 (1984), 225–262.
Escobar, J. F. andSchoen, R. M.,Conformal metrics with prescribed scalar curvature. Invent. Math.,86 (1986), 255–286.
Gilbarg, D. andTrudinger, N. S.,Elliptic Partial Differential Equations of Second Order. Springer Verlag, Berlin, 1983.
Heinze, E. andKarcher, H.,A general comparison theorem with applications to volume estimates for submanifolds. Ann. Scient. Ec. Norm. Sup.,11 (1978), 451–470.
Kazdan, J. L. andWarner, F. W.,Integrability conditions for Δu=k−K e 2u with applications to Riemannian geometry. Bull. Amer. Math. Soc.,77 (1971), 819–823.
Kazdan, J. L. andWarner, F. W.,Curvature functions for compact 2-manifolds. Annals of Math.,99 (1974), 14–47.
Moser, J.,A sharp form of an inequality by N. Trudinger. Indiana Math. J.,20 (1971), 1077–1092.
Moser, J.,On a nonlinear problem in differential geometry. InDynamical Systems ed. by M. Peixoto, Academic Press, New York, 1973.
O'Neil, R.,Convolution operators and L(p, q) spaces. Duke Math. J.,30 (1963), 129–142.
Schoen, R.,Conformal deformation of a Riemannian metric to constant scalar curvature. J. Differential Geometry,20 (1984), 479–495.
Stein, E.,Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, 1970.
Trudinger, N. S.,On embedding in Orlicz spaces and some applications. J. Math. Mech.,17 (1967), 473–484.
Wainger, S.,Special Trigonometric Series in k dimensions. Memoris of the American Mathematical Society n. 59, 1965.
Ziemer, W. P.,Weakly Differentiable Functions, Springer Verlag, Berlin, 1989.
Zygmund, A.,Trigonometric Series. Cambridge University Press, Cambridge, 1968.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fontana, L. Sharp borderline Sobolev inequalities on compact Riemannian manifolds. Commentarii Mathematici Helvetici 68, 415–454 (1993). https://doi.org/10.1007/BF02565828
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02565828