Skip to main content Accessibility help
×
Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T02:54:20.566Z Has data issue: false hasContentIssue false

1 - The supremum of first eigenvalues of conformally covariant operators in a conformal class

Published online by Cambridge University Press:  05 November 2011

Bernd Ammann
Affiliation:
Universität Regensburg
Pierre Jammes
Affiliation:
Université Nice – Sophia Antipolis
Roger Bielawski
Affiliation:
University of Leeds
Kevin Houston
Affiliation:
University of Leeds
Martin Speight
Affiliation:
University of Leeds
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] B., Ammann., The Dirac Operator on Collapsing Circle Bundles, Sém. Th. Spec. Géom Inst. Fourier Grenoble 16 (1998), 33–42.Google Scholar
[3] B., Ammann, The smallest Dirac eigenvalue in a spin-conformal class and cmc-immersions, Comm. Anal. Geom. 17 (2009), 429–479.Google Scholar
[4] B., Ammann, A spin-conformal lower bound of the first positive Dirac eigenvalue, Diff. Geom. Appl. 18 (2003), 21–32.Google Scholar
[5] B., Ammann, A variational problem in conformal spin geometry, Habilitationsschrift, Universitäat Hamburg, 2003.Google Scholar
[6] B., Ammann and C., Bäar, irac eigenvalues and total scalar curvature, J. Geom. Phys. 33 (2000), 229–234.Google Scholar
[7] B., Ammann and E., Humbert, The first conformal Dirac eigenvalue on 2-dimensional tori, J. Geom. Phys. 56 (2006), 623–642.Google Scholar
[8] B., Ammann, E., Humbert, and B., Morel, Mass endomorphism and spinorial Yamabe type problems, Comm. Anal. Geom. 14 (2006), 163–182.Google Scholar
[9] B., Ammann, A. D., Ionescu, and V., Nistor, Sobolev spaces on Lie manifolds and regularity for polyhedral domains, Doc. Math. 11 (2006), 161–206.Google Scholar
[10] B., Ammann, R., Lauter, and V., Nistor, On the geometry of Riemannian manifolds with a Lie structure at infinity, Int. J. Math. Math. Sci. (2004), 161–193.Google Scholar
[11] B., Ammann, Pseudodifferential operators on manifolds with a Lie structure at infinity, Ann. of Math. 165 (2007), 717–747.Google Scholar
[12] C., Bäar, The Dirac operator on space forms of positive curvature, J. Math. Soc. Japan 48 (1996), 69–83.Google Scholar
[13] C., Bäar, The Dirac operator on hyperbolic manifolds of finite volume, J. Differ. Geom. 54 (2000), 439–488.Google Scholar
[14] H., Baum, Spin-Strukturen und Dirac-Operatoren über pseudoriemannschen Mannigfaltigkeiten, Teubner Verlag, 1981.Google Scholar
[15] A. L., Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, no. 10, Springer-Verlag, 1987.Google Scholar
[16] T. P., Branson, Differential operators canonically associated to a conformal structure, Math. Scand. 57 (1985), 293–345.Google Scholar
[17] T. P., Branson, Group representations arising from Lorentz conformal geometry, J. Funct. Anal. 74 (1987), no. 2, 199–291.Google Scholar
[18] T. P., Branson, Second order conformal covariants, Proc. Amer. Math. Soc. 126 (1998), 1031–1042.Google Scholar
[19] B., Colbois and A. El, Soufi, Eigenvalues of the Laplacian acting on p-forms and metric conformal deformations, Proc. of Am. Math. Soc. 134 (2006), 715–721.Google Scholar
[20] A. El, Soufi and S., Ilias, Immersions minimales, première valeur propre du laplacien et volume conforme, Math. Ann. 275 (1986), 257–267.Google Scholar
[21] H. D., Fegan, Conformally invariant first order differential operators., Quart. J. Math. Oxford, II. series 27 (1976), 371–378.Google Scholar
[22] R., Gover and L. J., Peterson, Conformally invariant powers of the Laplacian, Q-curvature, and tractor calculus, Comm. Math. Phys. 235 (2003), 339–378.Google Scholar
[23] E., Hebey and F., Robert, Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients, Calc. Var. Partial Differential Equations 13 (2001), 491–517.Google Scholar
[24] N., Hitchin, Harmonic spinors, Adv. Math. 14 (1974), 1–55.Google Scholar
[25] P., Jammes, Extrema de valeurs propres dans une classe conforme, Sémin. Théor. Spectr. Géom. 24 (2007), 23–42.Google Scholar
[26] I., Kolář, P. W., Michor, and J., Slovák, Natural operations in differential geometry, Springer-Verlag, Berlin, 1993.Google Scholar
[27] N., Korevaar, Upper bounds for eigenvalues of conformal metrics, J. Differ. Geom. 37 (1993), 73–93.Google Scholar
[28] H.-B., Lawson and M.-L., Michelsohn, Spin Geometry, Princeton University Press, 1989.Google Scholar
[29] J. M., Lee and T. H., Parker. The Yamabe problem.Bull. Am. Math. Soc., New Ser. 17 (1987), 37–91.Google Scholar
[30] S. Mac, Lane, Categories for the working mathematician, Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998.Google Scholar
[31] R. B., Melrose, The Atiyah-Patodi-Singer index theorem, Research Notes in Mathematics, vol. 4, A K Peters Ltd., Wellesley, MA, 1993.Google Scholar
[32] S. M., Paneitz, A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds, Preprint 1983, published in SIGMA 4 (2008).Google Scholar
[33] M. E., Taylor, M. E., , Pseudodifferential operators, Princeton University Press, 1981.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×