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.
Categories: math.DG