Non-linear partial differential equations in conformal geometry

الأصل · EN

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 P₂ₖ with k ∈ N and k ≤ n/2 if the dimension n is even. Each P₂ₖ has leading order term (- Δ)ᵏ and is equal to (- Δ) ᵏ if the metric is flat.