# Sharp inequalities, the functional determinant, and the complementary series

@article{Branson1995SharpIT, title={Sharp inequalities, the functional determinant, and the complementary series}, author={T. Branson}, journal={Transactions of the American Mathematical Society}, year={1995}, volume={347}, pages={3671-3742} }

Results in the spectral theory of differential operators, and recent results on conformally covariant differential operators and on sharp inequalities, are combined in a study of functional determinants of natural differential operators. The setting is that of compact Riemannian manifolds. We concentrate especially on the conformally flat case, and obtain formulas in dimensions 2, 4, and 6 for the functional determinants of operators which are well behaved under conformai change of metric. The… Expand

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