Differential Geometry
Asymptotic expansion of the Faber–Krahn profile of a compact Riemannian manifold
Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1163-1167.

The aim of this Note is to give a proof of a well-known fact: an asymptotic expansion of the isoperimetric profile of a Riemannian manifold for small volumes gives an asymptotic expansion of the Faber–Krahn profile for this same Riemannian manifold.

Nous donnons dans cette Note la preuve d'un résultat bien connu : un développement limité du profil isopérimétrique d'une variété riemannienne donne un développement limité du profil de Faber–Krahn de cette même variété.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.09.022
Druet, Olivier 1

1 UMPA, ENS Lyon, 46, allée d'Italie, 69364 Lyon cedex 07, France
@article{CRMATH_2008__346_21-22_1163_0,
     author = {Druet, Olivier},
     title = {Asymptotic expansion of the {Faber{\textendash}Krahn} profile of a compact {Riemannian} manifold},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1163--1167},
     publisher = {Elsevier},
     volume = {346},
     number = {21-22},
     year = {2008},
     doi = {10.1016/j.crma.2008.09.022},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2008.09.022/}
}
TY  - JOUR
AU  - Druet, Olivier
TI  - Asymptotic expansion of the Faber–Krahn profile of a compact Riemannian manifold
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 1163
EP  - 1167
VL  - 346
IS  - 21-22
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2008.09.022/
DO  - 10.1016/j.crma.2008.09.022
LA  - en
ID  - CRMATH_2008__346_21-22_1163_0
ER  - 
%0 Journal Article
%A Druet, Olivier
%T Asymptotic expansion of the Faber–Krahn profile of a compact Riemannian manifold
%J Comptes Rendus. Mathématique
%D 2008
%P 1163-1167
%V 346
%N 21-22
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2008.09.022/
%R 10.1016/j.crma.2008.09.022
%G en
%F CRMATH_2008__346_21-22_1163_0
Druet, Olivier. Asymptotic expansion of the Faber–Krahn profile of a compact Riemannian manifold. Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1163-1167. doi : 10.1016/j.crma.2008.09.022. http://www.numdam.org/articles/10.1016/j.crma.2008.09.022/

[1] Bérard, P. Spectral Geometry: Direct and Inverse Problems, Lecture Notes in Mathematics, vol. 1207, Springer-Verlag, 1986

[2] Chavel, I. Eigenvalues in Riemannian Geometry, Pure and Applied Mathematics, vol. 115, Academic Press Inc., 1984

[3] Chavel, I. Riemannian Geometry – A Modern Introduction, Cambridge Tracts in Mathematics, vol. 108, Cambridge University Press, 1993

[4] Druet, O. Sharp local isoperimetric inequalities involving the scalar curvature, Proc. Amer. Math. Soc., Volume 130 (2002), pp. 2351-2361

[5] F. Pacard, P. Sicbaldi, Extremal domains for the first eigenvalue of the Laplace–Beltrami operator, Ann. Inst. Fourier, in press

Cited by Sources: