Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Explicit functional determinants in four dimensions


Authors: Thomas P. Branson and Bent Ørsted
Journal: Proc. Amer. Math. Soc. 113 (1991), 669-682
MSC: Primary 58G26; Secondary 47F05, 58E11, 58G11
MathSciNet review: 1050018
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Working on the four-sphere $ {S^4}$, a flat four-torus, $ {S^2} \times {S^2}$, or a compact hyperbolic space, with a metric which is an arbitrary positive function times the standard one, we give explicit formulas for the functional determinants of the conformal Laplacian (Yamabe operator) and the square of the Dirac operator, and discuss qualitative features of the resulting variational problems. Our analysis actually applies in the conformal class of any Riemannian, locally symmetric, Einstein metric on a compact $ 4$-manifold; and to any geometric differential operator which has positive definite leading symbol, and is a positive integral power of a conformally covariant operator.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58G26, 47F05, 58E11, 58G11

Retrieve articles in all journals with MSC: 58G26, 47F05, 58E11, 58G11


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1050018-8
PII: S 0002-9939(1991)1050018-8
Article copyright: © Copyright 1991 American Mathematical Society