Isoperimetric inequalities on compact manifolds

Geometriae Dedicata

Volumn 90, Issue 1, 2002, Pages 217-236

  Druet, Olivier ^a  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

Author keywords

Isoperimetric inequality; Optimal Sobolev inequalities

Indexed keywords

EID: 0141739320     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014977309741     Document Type: Article

References (25)

1. Almgren, F.: Existence and regularity almost everywhere of solutions to elliptic variational problems, Mem. Amer. Math. Soc. 165, vol. 4 (1976).
2. Aubin, T.: Problèmes isopérimétriques et espaces de Sobolev, J. Differential Geom. 11 (1976), 353-372.
3. Aubin, T. and Li, Y. Y.: On the best Sobolev inequality, J. Math. Pures Appl. 78 (1999), 353-387.
4. Bérard, P. and Meyer, D.: Inégalités isopérimétriques et applications, Ann. Sci. Ecole Norm. Sup. (4) 15(1982), 513-542.
5. Chavel, I.: Riemannian Geometry: A Modern Introduction, Cambridge Tracts in Math., Cambridge Univ. Press, 1993.
6. Croke, C. B.: A sharp four dimensional isoperimetric inequality, Comment. Math. Helv. 59 (1984), 187-192.
7. Djadli, Z. and Druet, O.: Extremal functions for optimal Sobolev inequalities on compact manifolds, Calc. Var. Partial Differential Equations 12 (2001), 59-84.
8. Druet, O.: The best constants problem in Sobolev inequalities, Math. Annal. 314 (1999), 327-346.
9. Druet, O.: Inégalités de Sobolev optimales: récents développements, Actes Sém. Théorie Spectrale et Géométrie Inst. Fourier 17, Université de Grenoble, 1999, pp. 111-127.
10. Druet, O.: Local isoperimetric inequalities on compact manifolds, Preprint, 2000.
11. Evans L. C. and Gariepy, R. F.: Measure Theory and Fine Properties of Functions, Stud. Adv. Math., CRC Press, Boca Raton, 1992.
12. Federer, H. and Fleming, W. H., Normal integral currents, Ann. Math. 72 (1960), 458-520.
13. Gallot, S.: Inégalités isopérimétriques et analytiques sur les variétés riemanniennes, Soc. Math. France, Astérisque 163-164 (1988), 31-91.
14. Gromov, M.: Paul Lévy's isoperimetric inequality, Preprint IHES, 1980.
15. Hebey, E.: Meilleures constantes et inégalités de Sobolev optimales sur les variétés Riemanniennes compactes, Actes Sém. Théorie Spectrale et Géométrie Inst Fourier 16, Université de Grenoble, 1998, pp. 175-210.
16. Hebey, E.: Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities, CIMS Lecture Notes 5, Courant Inst. Math. Sci., 1999.
17. Hebey, E. and Vaugon, M.: The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds, Duke Math. J. 79 (1995), 235-279.
18. Kleiner, B.: An isoperimetric comparison theorem, Invent. Math. 108 (1992), 37-47.
19. Ladyzhenskaya, O. A. and Uraltseva, N.: Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968.
20. Lions, P. L.: The concentration-compactness principle in the calculus of variations. The locally compact case. Part I, Ann. Inst. H. Poincaré 1 (1984), 109-145.
21. Osserman, R.: The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978), 1183-1238.
22. Serrin, J.: Local behavior of solutions of quasilinear equations, Acta Math. 111 (1964), 247-302.
23. Struwe, M.: Variational Methods, Ergeb. Math. Grenzgeb. 34, Springer-Verlag, New York, 1996.
24. Talenti, G.: Best constants in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976), 353-372.
25. Weil, A.: Sur les surfaces à courbure négative, CR Acad. Paris 182 (1926), 4069-1071.