The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Mass endomorphism, surgery and perturbations

Bernd Ammann[1]; Mattias Dahl[2]; Andreas Hermann[3]; Emmanuel Humbert[3]

  • [1] Fakultät für Mathematik Universität Regensburg 93040 Regensburg Germany
  • [2] Institutionen för Matematik Kungliga Tekniska Högskolan 100 44 Stockholm Sweden
  • [3] Laboratoire de Mathématiques et Physique Théorique, Université de Tours, Parc de Grandmont, 37200 Tours, France

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 2, page 467-487
  • ISSN: 0373-0956

Abstract

top
We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.

How to cite

top

Ammann, Bernd, et al. "Mass endomorphism, surgery and perturbations." Annales de l’institut Fourier 64.2 (2014): 467-487. <http://eudml.org/doc/275531>.

@article{Ammann2014,
abstract = {We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.},
affiliation = {Fakultät für Mathematik Universität Regensburg 93040 Regensburg Germany; Institutionen för Matematik Kungliga Tekniska Högskolan 100 44 Stockholm Sweden; Laboratoire de Mathématiques et Physique Théorique, Université de Tours, Parc de Grandmont, 37200 Tours, France; Laboratoire de Mathématiques et Physique Théorique, Université de Tours, Parc de Grandmont, 37200 Tours, France},
author = {Ammann, Bernd, Dahl, Mattias, Hermann, Andreas, Humbert, Emmanuel},
journal = {Annales de l’institut Fourier},
keywords = {Dirac operator; mass endomorphism; surgery; compact Riemannian spin manifolds; Dirac operators; mass endomorphisms},
language = {eng},
number = {2},
pages = {467-487},
publisher = {Association des Annales de l’institut Fourier},
title = {Mass endomorphism, surgery and perturbations},
url = {http://eudml.org/doc/275531},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Ammann, Bernd
AU - Dahl, Mattias
AU - Hermann, Andreas
AU - Humbert, Emmanuel
TI - Mass endomorphism, surgery and perturbations
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 2
SP - 467
EP - 487
AB - We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.
LA - eng
KW - Dirac operator; mass endomorphism; surgery; compact Riemannian spin manifolds; Dirac operators; mass endomorphisms
UR - http://eudml.org/doc/275531
ER -

References

top
  1. B. Ammann, A spin-conformal lower bound of the first positive Dirac eigenvalue, Diff. Geom. Appl. 18 (2003), 21-32 Zbl1030.58020MR1951070
  2. B. Ammann, The smallest Dirac eigenvalue in a spin-conformal class and cmc-immersions, Comm. Anal. Geom. 17 (2009), 429-479 Zbl1185.58013MR2550205
  3. B. Ammann, A variational problem in conformal spin geometry, (Habilitationsschrift, Universität Hamburg, 2003) Zbl1030.58020
  4. B. Ammann, M. Dahl, E. Humbert, Surgery and harmonic spinors, Adv. Math. 220 (2009), 523-539 Zbl1159.53021MR2466425
  5. B. Ammann, M. Dahl, E. Humbert, Harmonic spinors and local deformations of the metric, Comm. Anal. Geom. 18 (2011), 927-936 Zbl1257.53077MR2875865
  6. B. Ammann, J.-F. Grosjean, E. Humbert, B. Morel, A spinorial analogue of Aubin’s inequality, Math. Z. 260 (2008), 127-151 Zbl1145.53039MR2413347
  7. B. Ammann, E. Humbert, B. Morel, Mass endomorphism and spinorial Yamabe type problems, Comm. Anal. Geom. 14 (2006), 163-182 Zbl1126.53024MR2230574
  8. C. Bär, M. Dahl, Surgery and the Spectrum of the Dirac Operator, J. reine angew. Math. 552 (2002), 53-76 Zbl1017.58019MR1940432
  9. R. Beig, N. Ó Murchadha, Trapped surfaces due to concentration of gravitational radiation, Phys. Rev. Lett. 66 (1991), 2421-2424 Zbl0968.83504MR1104859
  10. J.-P. Bourguignon, P. Gauduchon, Spineurs, opérateurs de Dirac et variations de métriques, Comm. Math. Phys. 144 (1992), 581-599 Zbl0755.53009MR1158762
  11. T. Friedrich, Dirac Operators in Riemannian Geometry, 25 (2000), AMS, Providence, Rhode Island Zbl0949.58032MR1777332
  12. A. Hermann, Generic metrics and the mass endomorphism on spin 3-manifolds, Ann. Glob. Anal. Geom. 37 (2010), 163-171 Zbl1185.53014MR2578263
  13. A. Hermann, Dirac eigenspinors for generic metrics, (2012) 
  14. O Hijazi, Première valeur propre de l’opérateur de Dirac et nombre de Yamabe, C. R. Acad. Sci. Paris, Série I 313 (1991), 865-868 Zbl0738.53030MR1138566
  15. T. Kato, Perturbation theory for linear operators, 132 (1966), Springer-Verlag Zbl0531.47014MR203473
  16. H. B. Lawson, M.-L. Michelsohn, Spin geometry, (1989), Princeton University Press, Princeton Zbl0688.57001MR1031992
  17. J. M. Lee, T. H. Parker, The Yamabe problem, Bull. Am. Math. Soc., New Ser. 17 (1987), 37-91 Zbl0633.53062MR888880
  18. S. Maier, Generic metrics and connections on spin- and spin c -manifolds, Comm. Math. Phys. 188 (1997), 407-437 Zbl0899.53036MR1471821
  19. R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Diff. Geom. 20 (1984), 479-495 Zbl0576.53028MR788292
  20. S. Stolz, Simply connected manifolds of positive scalar curvature, Ann. of Math. (2) 136 (1992), 511-540 Zbl0784.53029MR1189863

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.