  In the study of conformal geometry, the method of elliptic partial
differential equations is playing an increasingly significant role. Since the
solution of the Yamabe problem, a family of conformally covariant operators
(for definition, see section 2) generalizing the conformal Laplacian, and their
associated conformal invariants have been introduced. The conformally covariant
powers of the Laplacian form a family $P_{2k}$ with $k \in \mathbb N$ and $k
\leq \frac{n}{2}$ if the dimension $n$ is even. Each $P_{2k}$ has leading order
term $(- \Delta)^k$ and is equal to $ (- \Delta) ^k$ if the metric is flat.
