Proceedings of the American Mathematical Society

Author(s): Olivier Druet
Journal: Proc. Amer. Math. Soc. 130 (2002), 2351-2361.
MSC (2000): Primary 49J40, 53C21
Posted: March 12, 2002
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Abstract: We provide sharp local isoperimetric inequalities on Riemannian manifolds involving the scalar curvature, and thus answer a question asked by Johnson and Morgan.

1.: T. Aubin, Problèmes isopérimétriques et espaces de Sobolev, J. Differential Geom. 11 (1976), 573-598. MR 56:6711
2.: T. Aubin and Y.Y. Li, On the best Sobolev inequality, J. Math. Pures Appl. 78 (1999), 353-387. MR 2000e:46041
3.: A. Beauville, Variétés Kähleriennes dont la première classe de Chern est nulle, J. Differential Geom. 18 (1983), 755-782.MR 86c:32030
4.: O. Druet, Optimal Sobolev inequalities of arbitrary order on compact Riemannian manifolds, J. Funct. Anal. 159 (1998), 217-242.MR 99m:53076
5.: -, The best constants problem in Sobolev inequalities, Math. Ann. 314 (1999), 327-346. MR 2000d:58033
6.: -, Isoperimetric inequalities on compact manifolds, Geometriae Dedicata (to appear).
7.: L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, CRC Press, 1992. MR 93f:28001
8.: E. Hebey, Nonlinear analysis on manifolds: Sobolev spaces and inequalities, CIMS Lecture Notes, vol. 5, Courant Institute of Mathematical Sciences, 1999.MR 2000e:58011
9.: -, Sharp Sobolev-Poincaré inequalities on compact Riemannian manifolds, Preprint (2000).
10.: D. Johnson and F. Morgan, Some sharp isoperimetric theorems for Riemannian manifolds, Indiana University Math. Journal 49, 3 (2000), 1017-1041.CMP 2001:06
11.: P.L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. Part I, Ann. Inst. H. Poincaré 1 (1984), 109-145. MR 87e:49035a
12.: -, The concentration-compactness principle in the calculus of variations. The limit case. Part I, Rev. Mat. Iberoamericano 1.1 (1985), 145-201. MR 87c:49007
13.: F. Morgan, Geometric Measure Theory : a Beginner's Guide, Academic Press, 1995.MR 96c:49001
14.: M. Struwe, Variational Methods, Ergebnisse der Mathematik und ihrer Grenzgebiete, 34, Springer, 1996.MR 98f:49002
15.: G. Talenti, Best constants in Sobolev inequality, Ann. Math. Pura Appl. 110 (1976), 353-372.MR 57:3846
16.: W.P. Ziemer, Weakly differentiable functions, Graduate Text in Mathematics, 120, Springer-Verlag, 1989. MR 91e:46046

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 49J40, 53C21

Olivier Druet
Affiliation: Département de Mathématiques, Université de Cergy-Pontoise, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France
Email: Olivier.Druet@math.u-cergy.fr

DOI: 10.1090/S0002-9939-02-06355-4
PII: S 0002-9939(02)06355-4
Received by editor(s): March 15, 2001
Posted: March 12, 2002
Communicated by: Jozef Dodziuk
Copyright of article: Copyright 2002, American Mathematical Society

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ISSN 1088-6826 (e) ISSN 0002-9939 (p)

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