Stability of the Faber-Krahn inequality in positive Ricci curvature

Jérôme Bertrand[1]

  • [1] Institut Fourier, BP 74, 38402 Saint-Martin d'Hères cedex (FRANCE)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 2, page 353-372
  • ISSN: 0373-0956

Abstract

top
P. Bérard and D. Meyer proved a Faber-Krahn inequality for domains in compact manifolds with positive Ricci curvature. We prove stability results for this inequality

How to cite

top

Bertrand, Jérôme. "Stabilité de l'inégalité de Faber-Krahn en courbure de Ricci positive." Annales de l’institut Fourier 55.2 (2005): 353-372. <http://eudml.org/doc/116194>.

@article{Bertrand2005,
abstract = {P. Bérard et D. Meyer ont démontré une inégalité du type Faber-Krahn pour les domaines d'une variété compacte à courbure de Ricci positive. Nous démontrons des résultats de stabilité associés à cette inégalité.},
affiliation = {Institut Fourier, BP 74, 38402 Saint-Martin d'Hères cedex (FRANCE)},
author = {Bertrand, Jérôme},
journal = {Annales de l’institut Fourier},
keywords = {Riemannian Geometry; Gromov-Hausdorff distance; Faber-Krahn inequality; convex domains},
language = {fre},
number = {2},
pages = {353-372},
publisher = {Association des Annales de l'Institut Fourier},
title = {Stabilité de l'inégalité de Faber-Krahn en courbure de Ricci positive},
url = {http://eudml.org/doc/116194},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Bertrand, Jérôme
TI - Stabilité de l'inégalité de Faber-Krahn en courbure de Ricci positive
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 2
SP - 353
EP - 372
AB - P. Bérard et D. Meyer ont démontré une inégalité du type Faber-Krahn pour les domaines d'une variété compacte à courbure de Ricci positive. Nous démontrons des résultats de stabilité associés à cette inégalité.
LA - fre
KW - Riemannian Geometry; Gromov-Hausdorff distance; Faber-Krahn inequality; convex domains
UR - http://eudml.org/doc/116194
ER -

References

top
  1. M. T. Anderson, Metrics of positive Ricci curvature with large diameter, Manuscripta Math. 68 (1990), 405-415 Zbl0711.53036MR1068264
  2. A.I. Ávila, Stability results for the first eigenvalue of the Laplacian on domains in space forms, J. Math. Anal. Appl. 267 (2002), 760-774 Zbl1189.35200MR1888036
  3. P. Bérard, D. Meyer, Inégalités isopérimétriques et applications, Ann. Sci. École Norm. Sup. 15 (1982), 513-541 Zbl0527.35020MR690651
  4. J. Bertrand, Pincement spectral en courbure de Ricci positive 
  5. J. Bertrand, Pincement spectral en courbure positive, (2003) 
  6. I. Chavel, E. A. Feldman, Spectra of domains in compact manifolds, J. Funct. Anal. 30 (1975), 198-222 Zbl0392.58016MR515225
  7. I. Chavel, Eigenvalues in Riemannian geometry, 115 (1984), Academic Press Inc., Orlando, FL Zbl0551.53001MR768584
  8. J. Cheeger, T. H. Colding, Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann. of Math. 144 (1996), 189-237 Zbl0865.53037MR1405949
  9. Shiu Yuen Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z. 143 (1975), 289-297 Zbl0329.53035MR378001
  10. S. Gallot, Inégalités isopérimétriques, courbure de Ricci et invariants géométriques, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), 365-368 Zbl0535.53035MR699164
  11. M. Gromov, Metric structures for Riemannian and non-Riemannian spaces, 152, Birkhäuser Boston Inc., Boston MA Zbl0953.53002MR1699320
  12. K. Grove, P. V. Petersen, A pinching theorem for homotopy spheres, J. Amer. Math. Soc. 3 (1990), 671-677 Zbl0717.53025MR1049696
  13. K. Grove, K. Shiohama, A generalized sphere theorem, Ann. Math. 106 (1977), 201-211 Zbl0341.53029MR500705
  14. P. Li, Shing Tung Yau, Estimates of eigenvalues of a compact Riemannian manifold, Geometry of the Laplace operator, XXXVI (1979), 205-239, Amer. Math. Soc., Providence R.I Zbl0441.58014
  15. J. Rauch, M. Taylor, Potential and scattering theory on wildly perturbed domains, J. Funct. Anal. 18 (1975), 27-59 Zbl0293.35056MR377303
  16. R. C. Reilly, Applications of the Hessian operator in a Riemannian manifold, Indiana Univ. Math. J. 26 (1977), 459-472 Zbl0391.53019MR474149

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.