Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 090, 31 pages      arXiv:0709.2471
Contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson

Q-Curvature, Spectral Invariants, and Representation Theory

Thomas P. Branson

Received August 01, 2007 from Xingwang Xu; Published online September 16, 2007

We give an introductory account of functional determinants of elliptic operators on manifolds and Polyakov-type formulas for their infinitesimal and finite conformal variations. We relate this to extremal problems and to the Q-curvature on even-dimensional conformal manifolds. The exposition is self-contained, in the sense of giving references sufficient to allow the reader to work through all details.

Key words: conformal differential geometry; functional determinant; conformal index.

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